# How does Hawking Radiation work exactly?

We are searching data for your request:

Forums and discussions:
Manuals and reference books:
Data from registers:
Wait the end of the search in all databases.
Upon completion, a link will appear to access the found materials.

I know that a particle and anti particle, virtual particles, spawn at the edge of an event horizon, and one particle falls into the black hole, and the other goes out, but how does the other know how to take energy from the black hole? I mean how does it? Does it just know to take energy from the black hole or does the antiparticle fall in, and the blackhole loses mass?

… but how does the other know how to take energy from the black hole?

In order to understand this, you need to be familiar with the essence of this picture$$^1$$ including negative energy states inside the horizon, creation of virtual particle-antiparticle pairs, and conservation of energy.$$^2$$ I try to intuitively answer your question with simple words.

Assume that a virtual particle-antiparticle pair is created near the black hole's horizon. According to the principle of conservation of energy, the total energy of the pair particles must be zero. So, one of the particle has positive energy and the other one has negative energy. On the other hand, it can be shown that there exist negative-energy states inside the horizon of a static black hole and the negative-energy particles can occupy these states. In order to have a pair of real particles with zero total energy, the only physical possibility is that the positive-energy particle can escape to infinity, while the negative-energy particle falls into the black hole. In this way, the strong gravitational field of the black hole can convert a virtual particle-antiparticle pair into a pair of real particles with zero total energy. This is the reason why the virtual particle that's sucked in always get negative energy. In this way, it is justified that the black hole loses its mass and gradually evaporates. (See the warning in the end of this answer, please.)

Does it just know to take energy from the black hole or does the antiparticle fall in, and the blackhole loses mass?

Note that, in this picture, when a virtual particle-antiparticle pair is created near the black hole's horizon, each of them may fall into the horizon or may escape to infinity (Always, one of them falls in and the other escapes.) So, it is not correct that only the antiparticle falls into the black hole. This means that a static observer outside the event horizon will observe both the particle and antiparticle spectrums.

Warning: In my opinion, you should not take the above argument about virtual particle-anti particle pair etc. too seriously since this picture helps to naively have an intuitive understanding. A rigorous treatment of Hawking radiation using quantization of quantum fields in curved black hole background does not need such a naïve picture.

$$^1$$There exist more rigorous treatments for understanding the Hawking radiation but I restrict myself to this framework (picture) that you are interested in and ask about.

$$^2$$ Here, for simplicity, I restrict this discussion to the case of static black holes. The general conclusion is still valid for the rotating black holes.

The name Stephen Hawking will forever be associated with a brilliant and inspirational scientist who helped come up with theories and explanations for some of the strangest mysteries in physics. One such theory, known as Hawking Radiation, could shed light on objects that frighten and fascinate us: black holes. Here’s what Hawking Radiation is and how it is theorized to work.

1. According to Hawking, black holes aren’t actually black.
The first and most essential thing to understand about Hawking Radiation is that it asserts that black holes, the objects we think of as sucking in all matter around them and letting nothing escape, actually do emit something—black body radiation.

2. The theory states that particle-antiparticle pairs are created at a black hole’s event horizon.
Quantum theory states that every particle has an antiparticle that acts as its opposite. These two usually annihilate one another, but in the case of Hawking radiation, they don’t. Instead, one falls into the black hole’s gravity, and the other is able to escape. That emitted particle has energy in the form of radiation, thus it appears that the black hole is emitting radiation instead of just absorbing it.

3. If this is the case, black holes lose mass.
While one particle is absorbed by the black hole, the other one escapes. This means the black hole is losing energy, and if it’s losing energy it’s losing mass. Therefore, black holes shouldn’t continue on forever. At some point they will lose all of their mass and, according to the theory, wink out of existence.

#### David-J-Franks

The name Stephen Hawking will forever be associated with a brilliant and inspirational scientist who helped come up with theories and explanations for some of the strangest mysteries in physics. One such theory, known as Hawking Radiation, could shed light on objects that frighten and fascinate us: black holes. Here’s what Hawking Radiation is and how it is theorized to work.

1. According to Hawking, black holes aren’t actually black.
The first and most essential thing to understand about Hawking Radiation is that it asserts that black holes, the objects we think of as sucking in all matter around them and letting nothing escape, actually do emit something—black body radiation.

2. The theory states that particle-antiparticle pairs are created at a black hole’s event horizon.
Quantum theory states that every particle has an antiparticle that acts as its opposite. These two usually annihilate one another, but in the case of Hawking radiation, they don’t. Instead, one falls into the black hole’s gravity, and the other is able to escape. That emitted particle has energy in the form of radiation, thus it appears that the black hole is emitting radiation instead of just absorbing it.

3. If this is the case, black holes lose mass.
While one particle is absorbed by the black hole, the other one escapes. This means the black hole is losing energy, and if it’s losing energy it’s losing mass. Therefore, black holes shouldn’t continue on forever. At some point they will lose all of their mass and, according to the theory, wink out of existence.

SaraRayne, If one particle falls into the black hole won't that increase its mass? The other particle that gets emitted is from the outside of the event horizon, not from the black hole itself. It looks to me like the black hole is extracting matter from space (quantum field/foam/fluctuations, aether, vacuum energy, dark energy or whatever) and getting bigger, not smaller! I don't understand! Please help.

Take a look at my book SaraRayne. With all the extra topics, my book is more than just a universe theory, so hopefully, provides a picture of existence which is complete, whole, (except for the minute details of every particle etc) and self-sufficient, requiring no creation or evolution and needs no beginning or end. With much of it based on solid scientific principles and good reasoning.

## From where (in space-time) does Hawking radiation originate?

According to my understanding of black hole thermodynamics, if I observe a black hole from a safe distance I should observe black body radiation emanating from it, with a temperature determined by its mass. The energy from this radiation comes from the black hole's mass itself.

But where (in space-time) does the process of generating the Hawking radiation happen? It seems like it should be at the event horizon itself. However, here is a Penrose diagram of a black hole that forms from a collapsing star and then evaporates, which I've cribbed from this blog post by Luboš Motl.

On the diagram I've drawn the world-lines of the star's surface (orange) and an observer who remains at a safe distance and eventually escapes to infinity (green). From the diagram I can see how the observer can see photons from the star itself and any other infalling matter (orange light rays). These will become red-shifted to undetectably low frequencies. But it seems as if any photons emitted from the horizon itself will only be observed at a single instant in time (blue light ray), which looks like it should be observed as the collapse of the black hole.

So it seems that if I observe photons from a black hole at any time before its eventual evaporation, they must have originated from a time before the horizon actually formed. Is this correct? It seems very much at odds with the way the subject of Hawking radiation is usually summarised. How is it possible for the photons to be emitted before the formation of the horizon? Does the energy-time uncertainty relation play a role here?

One reason I'm interested in this is because I'd like to know whether Hawking radiation interacts with the matter that falls in to the black hole. There seem to be three possibilities:

1. Hawking radiation is generated in the space-time in between the black hole and the observer, and so doesn't interact (much, or at all) with the infalling matter
2. Hawking radiation is generated near to the centre of the black hole, at a time before the horizon forms, and consequently it does interact with the matter.
3. The Hawking radiation is actually emitted by the infalling matter, which for some reason is heated to a very high temperature as it approaches the event horizon.
4. (With thanks to pjcamp) you can't think of them as coming from a particular point, because they are quantum particles and never have a well-defined location.

All these possibilities have quite different implications for how one should think of the information content of the radiation that eventually reaches the observer, so I'd like to know which (if any) is correct.

The fourth possibility does sound like the most reasonable, but if it's the case I'd like some more details, because what I'm really trying to understand is whether the Hawking photons can interact with the infalling matter or not. Ordinarily, if I observe a photon I expect it to have been emitted by something. If I observe one coming from a black hole, it doesn't seem unreasonable to try and trace its trajectory back in time and work out when and where it came from, and if I do that it will still appear to have come from a time before the horizon formed, and in fact will appear to be originating from surface of the original collapsing star, just before it passed the horizon. I understand the argument that the infalling matter will not experience any Hawking radiation, but I would like to understand whether, from the perspective of the outside observer, the Hawking radiation appears to interact with the matter falling into the black hole. Clearly it does interact with objects that are sufficiently far from the black hole, even if they're free-falling towards it, so if it doesn't interact with the surface of the collapsing star then where is the cutoff point, and why?

In an answer below, Ron Maimon mentions "a microscopic point right where the black hole first formed," but in this diagram it looks like no radiation from that point will be observed until the hole's collapse. Everything I've read about black holes suggests that Hawking radiation is observed to emanate from the black hole continuously, and not just at the moment of collapse, so I'm still very confused about this.

If the radiation is all emitted from this point in space-time, it seems like it should interact very strongly with the in-falling matter:

In this case, crossing the event horizon would not be an uneventful non-experience after all, since it would involve colliding with a large proportion of the Hawking photons all at once. (Is this related to the idea of a "firewall" that I've heard about?)

Finally, I realise it's possible that I'm just thinking about it in the wrong way. I know that the existence of photons is not observer-independent, so I guess it could just be that the question of where the photons originate is not a meaningful one. But even in this case I'd really like to have a clearer physical picture of the situation. If there is a good reason why "where and when do the photons originate?" is not the right question, I'd really appreciate an answer that explains it. (pjcamp's answer to the original version of the question goes some way towards this, but it doesn't address the time-related aspect of the current version, and it also doesn't give any insight as to whether the Hawking radiation interacts with the infalling matter, from the observer's perspective.)

Editorial note: this question has been changed quite a bit since the version that pjcamp and Ron Maimon answered. The old version was based on a time-symmetry argument, which is correct for a Schwartzchild black hole, but not for a transient one that forms from a collapsing star and then evaporates. I think the exposition in terms of Penrose diagrams is much clearer.

## Yes, Stephen Hawking Lied To Us All About How Black Holes Decay

Physicist and best-selling author Stephen Hawking presents a program in Seattle in 2012. Although he . [+] made some tremendous contributions to science, his analogy about black holes decaying has contributed to a generation of misinformed physicists, physics students, and physics enthusiasts.

The greatest idea of Stephen Hawking's scientific career truly revolutionized how we think about black holes. They're not completely black, after all, and it was indeed Hawking who first understood and predicted the radiation that they should emit: Hawking radiation. He derived the result in 1974, and it's one of the most profound links ever between the worlds of the quantum and our theory of gravitation, Einstein's General Relativity.

And yet, in his landmark 1988 book, A Brief History Of Time, Hawking paints a picture of this radiation — of spontaneously created particle-antiparticle pairs where one member falls in and the other escapes — that's egregiously incorrect. For 32 years, it's misinformed physics students, laypersons, and even professionals alike. Black holes really do decay. Let's make today the day we find out how they actually do it.

The features of the event horizon itself, silhouetted against the backdrop of the radio emissions . [+] from behind it, are revealed by the Event Horizon Telescope in a galaxy some 60 million light-years away. The dotted line represents the edge of the photon sphere, while the event horizon itself is interior even to that. Outside of the event horizon, a small amount of radiation is constantly emitted: Hawking radiation, which will eventually be responsible for this black hole's decay.

Event Horizon Telescope collaboration et al.

What Hawking would have had us imagine is a relatively simple picture. Start with a black hole: a region of space where so much mass has been concentrated into such a small volume that, within it, not even light can escape. Everything that ventures too close to it will inevitably be drawn into the central singularity, with the border between the escapable and inescapable regions known as the event horizon.

Now, let's add in quantum physics. Space, at a fundamental level, can never be completely empty. Instead, there are entities inherent to the fabric of the Universe itself — quantum fields — that are always omnipresent. And, just like all quantum entities, there are uncertainties inherent to them: the energy of each field at any location will fluctuate with time. These field fluctuations are very real, and occur even in the absence of any particles.

A visualization of QCD illustrates how particle/antiparticle pairs pop out of the quantum vacuum for . [+] very small amounts of time as a consequence of Heisenberg uncertainty. The quantum vacuum is interesting because it demands that empty space itself isn't so empty, but is filled with all the particles, antiparticles and fields in various states that are demanded by the quantum field theory that describes our Universe. Put this all together, and you find that empty space has a zero-point energy that's actually greater than zero.

In the context of quantum field theory, the lowest-energy state of a quantum field corresponds to no particles existing. But excited states, or states that correspond to higher-energies, correspond to either particles or antiparticles. One visualization that's commonly used is to think about empty space as being truly empty, but populated by particle-antiparticle pairs (because of conservation laws) that briefly pop into existence, only to annihilate away back into the vacuum of nothingness after a short while.

It's here that Hawking's famous picture — his grossly incorrect picture — comes into play. All throughout space, he asserts, these particle-antiparticle pairs are popping in and out of existence. Inside the black hole, both members stay there, annihilate, and nothing happens. Far outside of the black hole, it's the same deal. But right near the event horizon, one member can fall in while the other escapes, carrying real energy away. And that, he proclaims, is why black holes lose mass, decay, and where Hawking radiation comes from.

In Hawking's most famous book, A Brief History of Time, he makes the analogy that space is filled . [+] with particle-antiparticle pairs and that one member can escape (carrying positive energy) while the other falls in (with negative energy), leading to black hole decay. This flawed analogy continues to confuse generations of physicists and laypersons alike.

Ulf Leonhardt / University of St. Andrews

That was the first explanation that I, myself a theoretical astrophysicist, ever heard for how black holes decay. If that explanation were true, then that would mean:

1. Hawking radiation was composed of a 50/50 mix of particles and antiparticles, since which member falls and which one escapes will be random,
2. that all of the Hawking radiation, which causes black holes to decay, will be emitted from the event horizon itself, and
3. that every quantum of emitted radiation must have a tremendous amount of energy: enough to escape from almost, but not quite, being swallowed by the black hole.

Of course, all three of those points are not true. Hawking radiation is made almost exclusively of photons, not a mix of particles and antiparticles. It gets emitted from a large region outside the event horizon, not right at the surface. And the individual quanta emitted have tiny energies over quite a large range.

Both inside and outside the event horizon of a Schwarzschild black hole, space flows like either a . [+] moving walkway or a waterfall, depending on how you want to visualize it. But outside the event horizon, owing to the curvature of space, radiation is generated, carrying energy away and causing the mass of the black hole to slowly shrink over time.

Andrew Hamilton / JILA / University of Colorado

What's odd about this explanation is that it's not the one he used in the scientific papers he wrote concerning this topic. He knew that this analogy was flawed and would lead to physicists thinking incorrectly about it, but he chose to present it to the general public as though people weren't capable of understanding the real mechanism actually at play. And that's too bad, because the actual scientific story is no more complex, but far more illuminating.

Empty space really does have quantum fields all throughout it, and those fields really do have fluctuations in their energy values. There's a germ of truth in the "particle-antiparticle pair production" analogy, and it's this: in quantum field theory, you can model the energy of empty space by adding up diagrams that include the production of these particles. But it's a calculational technique only the particles and antiparticles are not real but are virtual instead. They are not actually produced, they do not interact with real particles, and they are not detectable by any means.

A few terms contributing to the zero-point energy in quantum electrodynamics. The development of . [+] this theory, due to Feynman, Schwinger, and Tomonaga, led to them being awarded the Nobel Prize in 1965. These diagrams may show particles and antiparticles popping in and out of existence, but that is only a calculational tool these particles are not real.

R. L. Jaffe, from https://arxiv.org/pdf/hep-th/0503158.pdf

To any observer located anywhere in the Universe, that "energy of empty space," which we call the zero-point energy, will appear to have the same value no matter where they are. However, one of the rules of relativity is that different observers will perceive different realities: observers in relative motion or in regions where the spacetime curvature is different, in particular, will disagree with one another.

So if you're infinitely far away from every source of mass in the Universe and your spacetime curvature is negligible, you'll have a certain zero-point energy. If someone else located at a black hole's event horizon, they'll have a certain zero-point energy that's the same measured value for them as it was for you infinitely far away. But if you try to map your zero-point energy to their zero-point energy (or vice versa), the values won't agree. From one another's perspectives, the zero-point energy changes relative to how severely the two spaces are curved.

An illustration of heavily curved spacetime for a point mass, which corresponds to the physical . [+] scenario of being located outside the event horizon of a black hole. As you get closer and closer to the mass's location in spacetime, space becomes more severely curved, eventually leading to a location from within which even light cannot escape: the event horizon. Observers at different locations will disagree as to what the zero-point energy of the quantum vacuum is.

Pixabay user JohnsonMartin

That's the key point behind Hawking radiation, and Stephen Hawking himself knew it. In 1974, when he famously derived Hawking radiation for the first time, this was the calculation he performed: calculating the difference in the zero-point energy in quantum fields from the curved space around a black hole to the flat space infinitely far away.

The results of that calculation are what determine the properties of the radiation that emanates from a black hole: not from the event horizon exclusively, but from the entirety of the curved space around it. It tells us the temperature of the radiation, which is dependent on the mass of the black hole. It tells us the spectrum of the radiation: a perfect blackbody, indicating the energy distribution of photons and — if there's enough energy available via E = mc² — massive particles and antiparticles, too.

The event horizon of a black hole is a spherical or spheroidal region from which nothing, not even . [+] light, can escape. But outside the event horizon, the black hole is predicted to emit radiation. Hawking's 1974 work was the first to demonstrate this, and it was arguably his greatest scientific achievement.

NASA DANA BERRY, SKYWORKS DIGITAL, INC.

It also enables us to compute an important detail that is not generally appreciated: where the radiation that black holes emit originates from. While most pictures and visualizations show 100% of a black hole's Hawking radiation being emitted from the event horizon itself, it's more accurate to depict it as being emitted over a volume that spans some 10-20 Schwarzschild radii (the radius to the event horizon), where the radiation gradually tapers off the farther away you get.

This leads us to a phenomenal conclusion: that all collapsed objects that curve spacetime should emit Hawking radiation. It may be a tiny, imperceptible amount of Hawking radiation, swamped by thermal radiation for as far as we can calculate for even long-dead white dwarfs and neutron stars. But it still exists: it's a positive, non-zero value that is calculable, dependent only on the object's mass, spin, and physical size.

As black holes lose mass due to Hawking radiation, the rate of evaporation increases. After enough . [+] time goes by, a brilliant flash of 'last light' gets released in a stream of high-energy blackbody radiation that favors neither matter nor antimatter.

The major problem with Hawking's explanation of his own theory is that he takes a calculational tool — the idea of virtual particles — and treats that tool as though it's equivalent to physical reality. In reality, what's happening is that the curved space around the black hole is constantly emitting radiation due to the curvature gradient around it, and that the energy is coming from the black hole itself, causing its event horizon to slowly shrink over time.

Black holes are not decaying because there's an infalling virtual particle carrying negative energy that's another fantasy devised by Hawking to "save" his insufficient analogy. Instead, black holes are decaying, and losing mass over time, because the energy emitted by this Hawking radiation is slowly reducing the curvature of space in that region. Once enough time passes, and that duration is enormous for realistic black holes, they will have evaporated entirely.

The simulated decay of a black hole not only results in the emission of radiation, but the decay of . [+] the central orbiting mass that keeps most objects stable. Black holes will only begin decaying in earnest, however, once the decay rate exceeds the growth rate. For the black holes in our Universe, that won't occur until the Universe is some 10 billion times its present age.

None of this should serve to take away from Hawking's tremendous accomplishments on this front. It was he who realized the deep connections between black hole thermodynamics, entropy, and temperature. It was he who put together the science of quantum field theory and the background of curved space near a black hole. And it was he who — quite correctly, mind you — figured out the properties and energy spectrum of the radiation that black holes would produce. It is absolutely fitting that the way black holes decay, via Hawking radiation, bears his name.

But the flawed analogy he put forth in his most famous book, A Brief History of Time, is not correct. Hawking radiation is not the emission of particles and antiparticles from the event horizon. It does not involve an inward-falling pair member carrying negative energy. And it shouldn't even be exclusive to black holes. Stephen Hawking knew how black holes truly decay, but he told the world a very different, even incorrect, story. It's time we all knew the truth instead.

## New possibilities for detecting Hawking radiation emitted by primordial black holes

New PBH constraint based on COMPTEL data (dark blue), projections of the discovery reach of future MeV gamma ray telescopes (other colored curves) and existing constraints (shaded grey regions). Credit: Coogan et al.

While many physicists have predicted the existence of dark matter, a type of matter that does not absorb, reflect or emit light, so far no one has been able to observe it experimentally or determine its fundamental nature. Light primordial black holes (PBHs), black holes the formed in the early universe, are among the most promising dark matter candidates. However, the existence of these black holes has not yet been confirmed.

Researchers at University of Amsterdam and University of California- Santa Cruz have recently carried out a study aimed at improving existing constraints on the allowed parameter space of PBHs as dark matter. In their paper, published in Physical Review Letters, they also propose a possible method that could be used to directly detect Hawking radiation in dark matter dense regions and potentially enable the discovery of PBH dark matter.

Hawking radiation is the thermal radiation that Stephen Hawking predicted to be spontaneously emitted by black holes. This radiation is hypothesized to arise from the conversion of quantum vacuum fluctuations into pairs of particles, one escaping the black hole and the other trapped inside its event horizon (i.e., the boundary around black holes from which no light or radiation can escape).

"PBHs comprising more than a few percent of the dark matter would need to have mass between about 10 16 grams and 10 35 grams," Adam Coogan, one of the researchers who carried out the study, told Phys.org. "Over most of that range, various observations exclude them from making up 100% of the dark matter. However, there is a notable gap in the constraints: PBHs with masses around that of an asteroid (

10 17 grams to 10 22 grams) could still make up all the dark matter."

Identifying methods to constrain the allowed parameter space of PBHs or detect the Hawking radiation emanating from them could be an important step towards the observation or discovery of PBH dark matter. Coogan, in collaboration with his colleagues Logan Morrison and Stefano Profumo, thus set out to examine the potential of MeV gamma-ray telescopes as tools to detect PBH Hawking radiation.

"The main idea behind our work was to think about a particular way of looking for asteroid-mass PBHs," Coogan explained. "Light PBHs are expected to emit Hawking radiation consisting of a mix of photons and other light particles, such as electrons and pions. Telescopes can then search for this radiation by observing our galaxy or other galaxies. The goal of our paper was to understand how well upcoming telescopes would be able to observe this radiation and consequentially how much of the asteroid-mass PBH parameter space they could probe."

While trying to estimate the masses of PBHs that emerging telescopes could help to constrain, Coogan and his colleagues discovered that previous studies had not yet analyzed data collected by the COMPTEL telescope, a gamma-ray telescope launched by NASA onboard of the Compton Gamma Ray Observatory (CGRO). This data, however, could help to constrain the abundance of PBHs slightly below the asteroid-mass gap (i.e., below 10 17 grams). While constraints already exist in this mass range thanks to observations of Hawking radiation gathered by Voyager 1 and the INTErnational Gamma-Ray Astrophysics Laboratory (INTEGRAL) satellite, the new constraints introduced by the researchers were found to be the strongest to date.

"The key input for computing constraints and making projections is to compute the spectrum of Hawking radiation produced by a single PBH," Coogan said. "We refined this calculation in comparison with existing tools in the literature by improving how radiation produced by electrons and pions is accounted for in the spectrum. The rest of the calculations are quite typical for dark matter searches."

Assuming that PBHs of a specific mass make up a given fraction of the total dark matter in space, the calculations carried out by Coogan and his colleagues would allow researchers to compute their contribution to the spectrum of photons emitted by an astrophysical object believed to contain a substantial amount of dark matter, such as the center of the Milky Way. If the spectrum estimated by these calculations was far brighter than the observed spectrum, for instance, one could rule out the possibility that PBHs of that specific mass make up a specific fraction of dark matter.

"Making projections for the performance of future telescopes follows along similar lines, though there is no observed spectrum to compare to," Coogan explained. "In this case, the spectrum of photons emitted by PBHs is compared with a model for the expected astrophysical background of photons."

The recent study by Coogan, Morrison and Profumo set the strongest constraints on low-mass PBHs to date, using data collected as part of an experiment that was completed 20 years ago. In addition, the researchers showed that upcoming telescopes capable of observing MeV-energy gamma rays could help to probe asteroid-mass PBHs, which is a very difficult part of the PBH parameter space to probe.

"The astronomy community has been considering several proposals for such telescopes in recent years and I think our paper provides another solid motivation for constructing them," Coogan added. "Aside from PBHs, we have been studying how upcoming MeV gamma-ray telescopes could probe different models of particle dark matter. We recently finished another paper where we computed the gamma-ray spectra for a few particular such models and are working with other collaborators to refine these calculations."

Coogan, Morrison and Profumo have recently also been collaborating with Alexander Moiseev, a Research Scientist at NASA, who is developing a telescope called the Galactic Explorer with a Coded Aperture Mask Compton Telescope (GECCO). Together with Moiseev, they have been trying to map out ways in which GECCO could aid the search for dark matter.

More information: Direct detection of Hawking radiation from Asteroid-mass primordial black holes. Physical Review Letters(2021). DOI: 10.1103/PhysRevLett.126.171101.

Precision gamma-ray constraints for Sub-GeV dark matter models. arXiv:2104.06168 [hep-ph]. arxiv.org/abs/2104.06168

Hunting for dark matter and new physics with (a) GECCO. arXiv:2101.10370 [astro-ph.HE]. arxiv.org/abs/2101.10370

Citation: New possibilities for detecting Hawking radiation emitted by primordial black holes (2021, June 21) retrieved 21 June 2021 from https://phys.org/news/2021-06-possibilities-hawking-emitted-primordial-black.html

This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission. The content is provided for information purposes only.

There is a better way of thinking about it.

Quantum mechanics says that there is some inherent uncertainty about what the location of a particle is or how much energy and momentum it has. It turns out that if you ask "how many particles are in this box" that's also an number that is fuzzy. It's not that there are twenty particles in the box, it's that the exact number of particles in the box is undefined. It's "around 20-ish."

Both the particle and anti-particle have positive mass.

Also the reason that something like Hawking radiation has to exist is that if you had a black hole suck everything, it would turn into an ultimate heat sink, and you could use it to create a perpetual motion machine.

Another problem I have with it, why would such a particle be able to escape anyway?

I mean we're talking at the edge of an event horizon with an escape velocity of slightly below light speed, how does any particle get away from there? Unless its a photon or a neutrino thats not pointing toward the black hole?

Anything else with mass, I have a hard time imagining it having enough momentum to get away from the black hole.

But then again, as far as I understand there has never been any proof of hawking radiation, so it could be a wrong assumption.

The way hawking Radiation works as I understand it, a pair is created on the edge of the event horizon, and as the pair is created, and before it can annihilate, the anti-particle falls into the black hole, and the positive particle is seen by the rest of the universe as if the black hole had just expelled matter.

Now, given how the uncertainty principle will never allow for any particle to have a known position, how can the black hole only absorb the anti-particle? Why isn't the black hole sometime getting the positive particle and therefore gaining weight? While the universe gets the bad end of the deal and gets an anti-particle?

and the link to Steve Carlip's explanation that I give in this post.

sorry to bring an old thread to the top, but i've been confused about the exact same thing as the OP, and luckily i found this thread via a search before unnecessarily starting my own. at any rate, after much thought of how particle-antiparticle pair creation near an event horizon can result in Hawking Radiation (BH evaporation), the most sensible explanation i could comtemplate in my own head was more or less what was stated above. if the gravitational field near the event horizon gives up a certain quantity of mass/energy in order to create the particle-antiparticle pair, then the BH's mass/energy must decrease by that same quantity. but the BH must gain some (but not all) of that mass/energy back when it swallows either one of the two particles previously created. that's the only way i can visualize hawking radiation as the actual decrease in the mass/energy of a BH. now granted, i don't expect anyone to be able to definitively confirm or deny my analysis - after all, we won't really know the specifics of the energy exchange until we start to actually witness Hawking Radiation. but i would like to hear from others on whether they generally agree or disagree with this notion of BH evaporation.

also, this blurb is a bit off-topic, but its somewhat related, so i thought i would postulate it here. i don't know if its possible, but i was wondering if the quantities of energy involved in the minute fluctuations of the BH's gravitational field that create these particle-antiparticle pairs in the first place could be small enough that neither particle of the pair is endowed with enough energy to escape the BH. if this scenario is possible (and i have no idea if it is or isn't), then it would seem that not all particle-antiparticle pair-creating fluctuations in the gravitatonal field result in Hakwing Radiation. that is, if the entire quantity of mass/energy given up by the BH during the creation of a particle-antiparticle pair is swallowed back up by the BH, then its mass/energy is conserved, and no mass/energy is radiated away in the form of Hakwing Radiation.

## The origin of Hawking radiation

Let us now explain the mechanism that is responsible for this thermal flux. It is to be found in the redshifting effect of Eq. (2) and the associated tearing apart of the light rays across the horizon of Eq. (). The exponential redshifting applies individually and universally to all light waves irrespectively of their initial frequency (Omega_0 .) A closer examination shows that every wave, in addition of being redshifted, is slightly amplified by this redshift. Moreover, it can be also shown that this amplification is necessarily accompanied by a correspondingly small production of a partner wave of opposite frequency. In classical terms, these two effects have no significant consequences because they are weighted by the amplitude of the partner wave (the coefficient ( eta_omega ) in Eq. (8) below) which is in general extremely small. On the contrary, in quantum mechanical terms this small amplification accompanied by the production of a partner wave is of uppermost importance as it is directly responsible for the Hawking effect. In quantum terms indeed, in the vacuum, the state of minimal energy, nothing would have happened without this amplification, i.e. black holes would have remained black.

Given the importance of this amplification, let us describe it with more precision. When considering the propagation of light in the static spacetime obtained after the collapse, one finds that outgoing wave packets initially localized very near the horizon split into two waves: one with positive frequency that escapes and a partner wave ( phi_ <-omega>) of negative frequency which is trapped inside the horizon: 2

There is a conservation law associated with the splitting that takes the form [ ag <9>vert alpha_omega vert^2 = 1 + vert eta_omega vert^2. ]

This law relates ( alpha_omega ,) the amplification factor of the escaping wave, to ( eta_omega ,) the amplitude of the partner wave which is trapped. Hawking showed that these coefficients obey [ ag <10>left| <eta_omega over alpha_omega > ight|^2 = e^ <- 2pi omega au_kappa >= e^<- hbar omega /k_B T_< m Hawking>>. ]

Recalling that the Boltzmann law of thermal equilibrium takes the form ( e^ <-E/k_BT> ,) and re-using the relation ( E = hbar omega ,) one can read from Eq. (10) the Hawking temperature of Eq. (5).

It now remains to understand what happens to the vacuum state when the amplification factor ( vert alpha_omega vert^2 > 1 ,) i.e. when ( eta_omega ) does not vanish. To this end, one must recall that the field describing quantum light does not strictly vanish in the vacuum. In fact, the field steadily fluctuates around a vanishing mean value. 3 In usual circumstances, these vacuum fluctuations remain unchanged, thereby expressing the stability of the vacuum state. However, when they are excited by some external agent, there can be a quantum transition which is accompanied by the emission of a photon, i.e. an excitation of the quantum field of light. For instance, when the light field is coupled to an excited atom, this causes the spontaneous decay of the atom and the emission of a photon. Similarly here, the redshifting effect of Eq. (2) excites some vacuum fluctuations and this leads to the steady production of photons. As for the spontaneous decay of atoms, the moments when the production occurs are randomly distributed. Indeed quantum mechanics only fixes the mean rate of their occurrence. A detailed calculation shows that this production rate is constant and fixed by ( vert eta_omegavert^2 ,) the squared norm of the partner wave coefficient that appears in Eqs. (8,9,10). For more details on this correspondence we refer to the review article [5].

Two important differences between atomic transitions and black hole radiation should be underlined. The first difference between coupling light to atoms and to the gravitational black hole field is that the latter necessarily leads to the production of pairs of photons. It can also be shown that in each pair, one photon escapes to spatial infinity and carries a positive energy ( hbar omega ,) whereas its partner carries a negative energy ( - hbar omega ,) and remains trapped inside the horizon. Moreover, in each pair, the two photons are "entangled", i.e. correlated with each other. Their entangled character can be revealed by studying non-local correlations across the black hole horizon. Doing so one obtains a spacetime pattern which is similar to that associated with the splitting of Eq. (8), see Figure 2. A second difference is that these pairs are steadily produced, one after the other, at the expense of the black hole mass. The black hole effectively behaves as an extremely excited atom that would have stored a huge amount of energy and would release it extremely slowly, as can be seen from Eq. (7) which gives the enormous lifetime of black holes. Taken together the escaping members of these pairs form a thermal flux at the Hawking temperature.

## How Stephen Hawking's Greatest Discovery Revolutionized Black Holes

The event horizon of a black hole is a spherical or spheroidal region from which nothing, not even . [+] light, can escape. But outside the event horizon, the black hole is predicted to emit radiation. Hawking's 1974 work was the first to demonstrate this, and it was arguably his greatest scientific achievement.

NASA DANA BERRY, SKYWORKS DIGITAL, INC.

In 1915, Albert Einstein published his General theory of Relativity, replacing our old Newtonian worldview with a unified concept of spacetime. On one side of Einstein's equations, the matter and energy in the Universe told spacetime how to curve on the other side, the curved fabric of spacetime told matter and energy how to move. The complicated nature of these equations ensured that exact solutions would be hard to find, as Einstein himself only ever found two: one for completely empty space and one for a single mass in the weak-field limit. The next year, Karl Schwarzschild found the first interesting solution, for a point mass over all of space. We now recognize this as the solution for a black hole, one of the few exact solutions known even today. While in Schwarzschild's formulation, black holes were static objects, Hawking was the first to prove that it isn't so. Black holes radiate over time, and as such, aren't even completely black.

The mass of a black hole is the sole determining factor of the radius of the event horizon, for a . [+] non-rotating, isolated black hole. For a long time, it was thought that black holes were static objects in the spacetime of the Universe.

It's been known for a long time that there are only a few properties that can describe a black hole. In Schwarzschild's case, he simply assigned it mass, and solved for the curvature of spacetime. It was shown by others that you could add a charge (Reissner–Nordström black holes) or a spin (Kerr black holes), but that was it. What you couldn't do was add information into a black hole: an electrically neutral, non-rotating human being contained as much information as an equivalent cloud of hydrogen gas once it entered a black hole. From a thermodynamic point-of-view, this was a disaster. You could throw a cloud of hydrogen gas with a temperature of absolute zero, and hence an entropy of zero, into the black hole, and it would have the same effect on the black hole as throwing an equivalent-energy human being in there. This simply didn't make sense.

When a mass gets devoured by a black hole, the amount of entropy the matter has is determined by its . [+] physical properties. But inside a black hole, only properties like mass, charge, and angular momentum matter. This poses a big conundrum if the second law of thermodynamics must remain true.

Illustration: NASA/CXC/M.Weiss X-ray (top): NASA/CXC/MPE/S.Komossa et al. (L) Optical: ESO/MPE/S.Komossa (R)

It meant that, contrary to the second law of thermodynamics, it meant we suddenly had a way to arbitrarily decrease the entropy of the Universe. A black hole, classically, should have an entropy of zero. If you could throw objects with real, positive, and large amounts of entropy into a black hole, you'd have a way to violate that law. Entropy always increases, as far as we know, and this was one of the things Hawking was thinking about when he was considering what was puzzling about black holes. There must be some way to define it for black holes, and that value ought to be both positive and large. Increasing entropy, over time, should be okay, but decreasing it should be forbidden. The only way to ensure that would be by forcing an increase in the black hole's mass to cause entropy to go up by at least the largest amount you can imagine.

Encoded on the surface of the black hole can be bits of information, proportional to the event . [+] horizon's surface area.

T.B. Bakker / Dr. J.P. van der Schaar, Universiteit van Amsterdam

The way that people working on that problem – including Hawking – assigned an answer was to make entropy proportional to the surface area of a black hole. The more quantum bits of information you can fit on a black hole, the greater its entropy was. But that brought up a new problem: if you have entropy, then that means you have a temperature. And if you have a temperature, you have to radiate energy away. Originally called "black" because nothing, not even light, can escape, now it became clear it had to emit something after all. All of a sudden, a black hole isn't a static system anymore it's one that changes over time.

The simulated decay of a black hole not only results in the emission of radiation, but the decay of . [+] the central orbiting mass that keeps most objects stable. Black holes are not static objects, but rather change over time.

So if a black hole isn't so black, and if it's radiating, the big question now becomes how. How does a black hole radiate? Figuring out the answer to this conundrum was Hawking's biggest contribution to physics. We know how to calculate, in quantum field theory, how the vacuum of empty space behaves when space is flat. That is, we can tell you properties of empty space when you're very far away from any masses, like a black hole. What Hawking showed, for the first time, is how to do this in curved space: within a few radii of the event horizon. And what he found was that there was a marked difference in the behavior of the quantum vacuum when a mass was near.

Quantum gravity tries to combine Einstein’s general theory of relativity with quantum mechanics. . [+] Quantum corrections to classical gravity are visualized as loop diagrams, as the one shown here in white. The semiclassical approximation that Hawking used involved calculating the quantum field theoretic effects of the vacuum in the background of curved space.

SLAC National Accelerator Lab

When he ran through the math, he found the following properties:

• When you're far from the black hole, it looks like you get the thermal emission of blackbody radiation.
• The temperature of the emission is dependent on the black hole's mass: the lower the mass, the higher the temperature.
• As the black hole emits radiation, it decreases in mass, in exact accord with Einstein's E = mc 2 . The higher the rate of radiation, the faster the mass loss.
• And as the black hole loses mass, it shrinks and radiates faster. The time a black hole can live is proportional to its mass cubed: the black hole at the Milky Way's center will live some 10 20 times longer than a black hole of the Sun's mass.

If you visualize empty space as frothing with particle/antiparticle pairs that pop in-and-out of . [+] existence, you'll see radiation coming from the black hole. This visualization is not quite correct, but the fact that it's easy to visualize has its benefits.

Ulf Leonhardt of the University of St. Andrews

Originally, Hawking visualized this as particle/antiparticle pairs popping in-and-out of existence, annihilating away to produce radiation. That oversimplified picture was qualitatively good enough to describe the radiation far from the black hole, but it turns out to be incorrect close to the event horizon. It's more accurate to think of the vacuum changing, and of the radiation as being emitted from wherever the curvature of space is relatively large: within a few radii of the black hole itself. Once you get far away, though, everything just appears to be this thermal, blackbody radiation.

Hawking radiation is what inevitably results from the predictions of quantum physics in the curved . [+] spacetime surrounding a black hole's event horizon. This visualization is more accurate than the above, since it shows photons as the primary source of radiation rather than particles. However, the emission is due to the curvature of space, not the individual particles, and doesn't all trace back to the event horizon itself.

All at once, there was a revolution in black holes, and in understanding how quantum fields behave in highly curved space. It opened up the black hole information paradox, as we're now asking where the information encoded on the black hole's event horizon goes when a black hole evaporates? It opens up the (related) problem of black hole firewalls, asking why don't objects get fried by radiation as they cross the event horizon, or whether they in fact do? It tells us there's a relationship between what happens within a volume (in the space enclosed by the event horizon) and the surface encapsulating it (the event horizon itself), which is a potential example of the holographic principle in real life. And it opens the door to additional subtleties that may allow us, for the first time, to probe the effects of quantum gravity if there are any departures from the predictions of General Relativity.

Against a seemingly eternal backdrop of everlasting darkness, a single flash of light will emerge: . [+] the evaporation of the final black hole in the Universe.

The paper that led to all this was simply titled Black Hole Explosions? and was published in Nature back in 1974. It would have been the crowning achievement of a lifetime of research, and Hawking published it when he was merely 32 years old. He had been researching singularities, black holes, baby universes, and the Big Bang for many years, having collaborated with titans like Gary Gibbons, George Ellis, Dennis Sciama, Jim Bardeen, Roger Penrose, Bernard Carr, and Brandon Carter, to name a few. His brilliant work didn't come out of nowhere, but arose out of a combination of a brilliant mind thriving in a fertile academic environment. It's a lesson to us all in how important it is, if we want to have these titanic theoretical advances, to create (and fund) these quality environments where research like this can come to life.

Outside the event horizon of a black hole, General Relativity and quantum field theory are . [+] completely sufficient for understanding the physics of what occurs that is what Hawking radiation is.

Nearly half a century later, the world mourns his passing, but the legacy of his research lives on. Perhaps this will be the century where there paradoxes are resolved, and the next titanic leaps forward in physics are taken. Regardless of what the future holds, Hawking's legacy is secure, and the most any theorist can hope for is that their theories will be improved in time. As Hawking himself stated:

Any physical theory is always provisional, in the sense that it is only a hypothesis: you can never prove it. No matter how many times the results of experiments agree with some theory, you can never be sure that the next time the result will not contradict the theory.

While the world may have lost one of its great scientific luminaries with Hawking's demise, his impact on our knowledge, understanding, and curiosity will echo throughout the ages.

## STEPHEN HAWKING

Stephen Hawking is a world-renowned British theoretical physicist, known for his contributions to the fields of cosmology, general relativity and quantum gravity, especially in the context of black holes. In the 1960s and 1970s, he worked on ground-breaking theorems regarding singularities within the framework of general relativity, and made the theoretical prediction that black holes should emit radiation (known today as Hawking radiation). He has also published several works of popular science in which he discusses his own theories and cosmology in general, including the runaway bestseller “A Brief History of Time”, and has come to be thought of as one of the greatest minds in physics since Albert Einstein. In his own words: “My goal is simple. It is complete understanding of the universe, why it is as it is and why it exists at all”.

Stephen William Hawking was born on 8 January 1942 in Oxford, England, in the middle of World War II. After his birth in the relative safety of Oxford, the family moved back to London, where his father headed the division of parasitology at the National Institute for Medical Research, despite the continued risk of bombing from the German air forces. In 1950, Hawking moved with his family to St. Albans, where he attended St. Albans High School for Girls from 1950 to 1953 (boys could attend until the age of 10), and from the age of 11, he attended St. Albans School, where he was a good, but not an exceptional, student.

In 1959, he won a scholarship to University College, Oxford, his father's old college, where he studied physics under Robert Berman (mainly because his own preference, mathematics, was not offered there), where he pursued his particular interests in thermodynamics, relativity, and quantum mechanics. Despite his sometimes lax study habits and his boredom with university life, he graduated in 1962 with a First Class BA degree.

After graduating from Oxford, he spent a short time studying sunspots at Oxford University’s observatory. However, he soon realized that he was more interested in theory than in observation, and left Oxford for Trinity Hall, Cambridge, where he studied for a time under Fred Hoyle, the most distinguished English astronomer of the time.

Soon after arriving at Cambridge, at the age of 21, Hawking started to develop the first symptoms of amyotrophic lateral sclerosis (ALS or “Lou Gehrig's disease”), a type of motor neurone disease which would eventually cost him almost all neuromuscular control. Although doctors predicted (incorrectly, as it turned out) that Hawking would not survive more than two or three years, he did gradually lose the use of his arms, legs and voice, until he was almost completely paralysed and quadriplegic.

Crucially, in 1965, he attended a lecture by the English mathematician Roger Penrose, who had recently produced a ground-breaking paper on space-time singularities (events in which the laws of physics seem to break down). Hawking became re-energized and engaged with renewed vigour in the study of theoretical astronomy and cosmology, particularly in the area of black holes and singularities. He would later collaborate with Penrose on several important papers on these subjects.

Another turning point in his life also occurred in 1965, with his marriage to a language student, Jane Wilde. With her help, and that of his doctoral tutor, Dennis Sciama, Hawking went on to complete his PhD and to become a Research Fellow and, later, a Professorial Fellow at Gonville and Caius College, Cambridge.

In 1968, he joined the staff of the Institute of Astronomy in Cambridge, where he remained until 1973, and began to apply the laws of thermodynamics to black holes by means of very complicated mathematics. In the late 1960s, he and his Cambridge friend and colleague, Roger Penrose, applied a new, complex mathematical model they had created from Albert Einstein's General Theory of Relativity which led, in 1970, to Hawking proving the first of many singularity theorems. This theorem provided a set of sufficient conditions for the existence of a singularity in space-time, and also implied that space and time would indeed have had a beginning in a Big Bang event, and would end in black holes. In effect, he had reversed Penrose's idea that the creation of a black hole would necessarily lead to a singularity, proving that it was a singularity that led to the creation of the universe itself.

In collaboration with Brandon Carter, Werner Israel and David Robinson, he provided a mathematical proof of John Wheeler's so-called "No-Hair Theorem", that any black hole is fully described by the three properties of mass, angular momentum and electric charge, and proposed the four laws of black hole mechanics, similar to the four classical Laws of Thermodynamics. From analysis of gamma ray emissions, he also suggested that primordial or “mini black holes” would have been formed after the Big Bang.

In 1974, Hawking and Jacob Bekenstein showed that black holes are not actually completely black, but that they should thermally create and emit sub-atomic particles, known today as Hawking radiation, until they eventually exhaust their energy and evaporate. This also resulted in the so-called “Information Paradox” or “Hawking Paradox”, whereby physical information (which roughly means the distinct identity and properties of particles) appears to be completely lost to the universe, in contravention of the accepted laws of physics. Hawking defended this paradox against the arguments of Leonard Susskind and others for thirty years, until famously retracting his claim in 2004.

These cutting edge achievements were made despite the increasing paralysis caused by Hawking's ALS. By 1974, he was unable to feed himself or get out of bed, and his speech became so slurred that he could only be understood by people who knew him well. In 1985, he caught pneumonia and had to have a tracheotomy, which left him unable to speak at all, although although a variety of friends and well-wishers collaborated in building him a device that enabled him to write onto a computer with small movements of his body, and then to speak what he had written using a voice synthesizer.

In 1973, he left the Institute of Astronomy for the Department of Applied Mathematics and Theoretical Physics and, in 1979, he was appointed Lucasian Professor of Mathematics at Cambridge University, a post he was to retain for 30 years until his retirement in 2009. He had three children with Jane Wilde: Robert (1967), Lucy (1969) and Timothy (1979), but the couple finally separated in 1991, reportedly due to the pressures of Hawking’s fame and his increasing disability.

Hawking’s ground-breaking research resulted in considerable fame and celebrity. In 1974, at the age of 32, he was elected as one of the youngest ever Fellows of the Royal Society. He was created a Commander of the Order of the British Empire (CBE) in 1982, and became a Companion of Honour in 1989. He has accumulated twelve honorary degrees, as well as many other awards, medals and prizes, including the Albert Einstein Award, the most prestigious in theoretical physics. He also became well-known among a wider audience, especially after his 1988 international bestselling book “A Brief History of Time”, and its follow ups “The Universe in a Nutshell” (2001) and “A Briefer History of Time” (2005).

He continued lines of research into exploding black holes, string theory, and the birth of black holes in our own galaxy. His work also increasingly indicated the necessity of unifying general relativity and quantum theory in an all-encompassing theory of quantum gravity, a so-called "theory of everything", particularly if we are explain what really happened at the moment of the Big Bang. As early as 1974, his theory of the emission of Hawking radiation from black holes was perhaps one of the first ever examples of a theory which synthesized, at least to some extent, quantum mechanics and general relativity

Among the myriad other scientific investigations pursued by Hawking over the years are the study of quantum cosmology, cosmic inflation, helium production in anisotropic Big Bang universes, "large N" cosmology, the density matrix of the universe, the topology and structure of the universe, baby universes, Yang-Mills instantons and the S matrix, anti-de Sitter space, quantum entanglement and entropy, the nature of space and time and the arrow of time, spacetime foam, string theory, supergravity, Euclidean quantum gravity, the gravitational Hamiltonian, the Brans-Dicke and Hoyle-Narlikar theories of gravitation, gravitational radiation, holography, time symmetry and wormholes.

Never afraid to court controversy, he even began to question the Big Bang theory itself in the 1980s, suggesting that perhaps there never was a start and would be no end, but just change, a constant transition of one "universe" giving way to another through glitches in space-time. He developed his "No Boundary Proposal" in collaboration with the Amercian physicist Jim Hartle. Under classical general relativity, the universe either has to be infinitely old or had to have started at a singularity, but Hawking and Hartle’s proposal raises a third possibility: that the universe is finite but had no initial singularity to produce a boundary. The history of this no-boundary universe in "imaginary time" can perhaps be best envisaged using the analogy of the surface of Earth, with the Big Bang equivalent to Earth’s North Pole, and the size of the universe increasing with imaginary time as you head south toward the equator.

In 1995, Hawking married his nurse, Elaine Mason, although they divorced in 2006 amid unconfirmed rumours of physical abuse, and he has since made up his differences with his first wife, Jane. In 2003, Hawking became dangerously ill with pneumonia, before confounding his doctors once again by recovering and throwing himself ever more emphatically into his work.

In 2004, he dramatically reversed one of his earlier controversial claims about black holes (that they destroy everything that falls into them and that no information is ever retrieveable from a black hole), claiming new findings that could help solve the so-called “black hole information paradox”. In his new definition of black holes, the event horizon is not so well-delineated and may not completely hide everything within it from the outside, and he has embraced the concept of the multiverse to help explain the conservation of information in black holes.

Hawking's views on the existence of God have been the subject of much debate, especially since his 1988 "A Brief History of Time" in which he mused that the discovery of an overarching theory of everything would allow us to "know the mind of God", which some people have interpreted as literal and some as literary. However, in his 2010 book "The Grand Design" he states unequivocally that "spontaneous creation is the reason there is something rather than nothing, why the universe exists, why we exist. It is not necessary to invoke God. to set the universe going".

Hawking retired from his position as Lucasian Professor of Mathematics at Cambridge in 2009, in accordance with the University's retirement policy, and accepted a Distinguished Research Chair at the Perimeter Institute for Theoretical Physics in Waterloo, Canada. In the same year, he was awarded the Presidential Medal of Freedom, the highest civilian award in the United States.

Stephen Hawking died at age 76 on March 13, 2018.