# Mathematical Analysis of Blackhole

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Mathematically, for black holes old enough that the stellar material has collapsed all the way into the singularity, the region between the horizon and the singularity is occupied by a spacetime where the time and space coordinates are reversed from those of the outside world. What this means in terms of what you experience is unknown. Other more complex conditions can occur of the black hole is rotating. In that case the singularity becomes a ring around the center of the black hole. You can pass through the center, but the tidal gravitational field would be lethal in all likelihood. In nearly all cases there would be gravitational radiation rattling about, and this would cause distortions in spacetime that would probably lead to spectacular optical distortions.

My question is Black hole absorbs everything. Is there any mathematical proof regarding this?

The Schwarzschild metric can be written as $$c^2 d au^2 = left( 1 - frac{r_s}{r} ight) dt^2 - left(1 - frac{r_s}{r} ight)^{-1} dr^2 -… ,$$ where $$r$$ is the radial coordinate, $$t$$ is the coordinate time, $$au$$ is the proper time (that measured on an observer's own clock) and $$r_s = 2GM/c^2$$ is the Schwarzschild radius. I have left out the angular terms on the right hand side which contribute a further negative term independent of whether $$r$$ is greater or less than $$r_s$$.

For an observer with mass, $$d au>0$$; for a massless particle $$d au=0$$ (e.g. a photon).

When $$r<>$$ the first term on the RHS is negative, while the second term becomes positive. In order for the LHS to be $$geq 0$$, then $$left(frac{r_s}{r}-1 ight)^{-1} dr^2 geq left(frac{r_s}{r}-1 ight) dt^2 +…$$ $$left| frac{dr}{dt} ight| geq left(frac{r_s}{r} -1 ight)$$

What this means is that $$dr/dt$$ can never be zero, which means the direction of radial travel can never reverse. ie. Anything that enters a black hole (i.e. for which $$r<>$$) and has $$dr/dt<0$$, can never have $$dr/dt >0$$.

There is a slightly more satisfactory "proof" using Eddington-Finkelstein coordinates, that shows that all future light cones point inwards and that $$dr<0$$ when $$r<>$$.

## Pierre-Simon Laplace

Pierre-Simon, marquis de Laplace ( / l ə ˈ p l ɑː s / French: [pjɛʁ simɔ̃ laplas] 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized and extended the work of his predecessors in his five-volume Mécanique Céleste (Celestial Mechanics) (1799–1825). This work translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems. In statistics, the Bayesian interpretation of probability was developed mainly by Laplace. [2]

Laplace formulated Laplace's equation, and pioneered the Laplace transform which appears in many branches of mathematical physics, a field that he took a leading role in forming. The Laplacian differential operator, widely used in mathematics, is also named after him. He restated and developed the nebular hypothesis of the origin of the Solar System and was one of the first scientists to postulate the existence of black holes and the notion of gravitational collapse.

Laplace is remembered as one of the greatest scientists of all time. Sometimes referred to as the French Newton or Newton of France, he has been described as possessing a phenomenal natural mathematical faculty superior to that of any of his contemporaries. [3] He was Napoleon's examiner when Napoleon attended the École Militaire in Paris in 1784. Laplace became a count of the Empire in 1806 and was named a marquis in 1817, after the Bourbon Restoration.

## Fingerprint Dive into the research topics of 'The mathematical analysis of black holes in general relativity'. Together they form a unique fingerprint.

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Invited Lectures. ed. / Sun Young Jang Young Rock Kim Dae-Woong Lee Ikkwon Yie. KYUNG MOON SA Co. Ltd., 2014. p. 747-772 (Proceeding of the International Congress of Mathematicans, ICM 2014 Vol. 3).

Research output : Chapter in Book/Report/Conference proceeding › Conference contribution

T1 - The mathematical analysis of black holes in general relativity

N2 - The mathematical analysis of black holes in general relativity has been the focus of considerable activity in the past decade from the perspective of the theory of partial differential equations. Much of this work is motivated by the problem of understanding the two celebrated cosmic censorship conjectures in a neighbourhood of the Schwarzschild and Kerr solutions. Recent progress on the behaviour of linear waves on black hole exteriors as well as on the full non-linear vacuum dynamics in the black hole interior puts us at the threshold of a complete understanding of the stability-and instability-properties of these solutions. This talk will survey some of these developments.

AB - The mathematical analysis of black holes in general relativity has been the focus of considerable activity in the past decade from the perspective of the theory of partial differential equations. Much of this work is motivated by the problem of understanding the two celebrated cosmic censorship conjectures in a neighbourhood of the Schwarzschild and Kerr solutions. Recent progress on the behaviour of linear waves on black hole exteriors as well as on the full non-linear vacuum dynamics in the black hole interior puts us at the threshold of a complete understanding of the stability-and instability-properties of these solutions. This talk will survey some of these developments.

## How to ‘seed’ supermassive black holes in the early universe

An artist’s impression of a supermassive black hole surrounded by a vast disc of gas and dust. Image: NASA/JPL-Caltech

A major question mark about the evolution of the early universe is how supermassive black holes managed to form in the first 800 million years or so of the Big Bang. According to conventional wisdom, supermassive black holes form in the central regions of a galaxy and grow primarily by capturing surrounding gas, a process that occurs over long time scales.

But doctoral student Lumen Boco and his advisor Andrea Lapi, both at the Scuola Internazionale Superiore di Studi Avanzati (International School for Advanced Studies) in Trieste, Italy, say they have been able to show, through an analysis published in The Astrophysical Journal, that earlier models for accelerated growth are, in fact, possible.

They began with early galaxies, progenitors of more evolved elliptical galaxies, with a very high gas content.

Such galaxies would have hosted extremely intense waves of early star formation, giving birth to massive suns that quickly burned through their nuclear fuel, exploded in supernova blasts and collapsed to form stellar-mass black holes. The dense gas in those galaxies would have caused them to migrate inward toward the centre of their host galaxy where they could merge to form the “seed” of a supermassive black hole.

“The biggest stars live a short time and very quickly evolve into stellar black holes, as large as several scores of solar masses,” Boco and Lapi write. “They are small, but many form in these galaxies. Our numerical calculations show that the process of dynamic migration and fusion of stellar black holes can make the supermassive black hole seed reach a mass of between 10,000 and 100,000 times that of the Sun in just 50-100 million years.”

Staring from such an initially massive seed, the black hole’s growth by accretion of surrounding gas is accelerated, explaining the presence of such massive black holes in the early universe.

“Starting from such a big seed as envisaged by our mechanism speeds up the global growth of the supermassive black hole and allows its formation … in the young universe. In
short, in light of this theory, we can state that 800 million years after the Big Bang the supermassive black holes could already populate the Cosmos.”

While their conclusion is based on a mathematical analysis, Boco and Lapi say their theory can be tested.

“The fusion of numerous stellar black holes with the seed of the supermassive black hole at the centre will produce gravitational waves, which we expect to see and study with current and future detectors,” the researchers said.

## Researchers Have Found A New Way To Turn A Black Hole Into A Power Station

Nothing can escape a black hole once it has crossed its event horizon but mathematical analysis over the last several decades has shown that there are ways to extract energy from a rotating black hole. Researchers have now revealed new work presenting an innovative way to harness energy out of a black hole, publishing their findings in Physical Review D.

Mathematically speaking, if a black hole rotates then it has an ergosphere. This is a region outside its event horizon (the threshold where to escape the pull of the black hole you’d need to move faster than the speed of light) where it is theoretically possible to steal some of the black hole's energy. Stephen Hawking worked out ways that quantum mechanics can remove energy from black holes. Nobel physicist Roger Penrose has a more mechanical approach that requires following particular orbits. The new work focuses on magnetic fields.

The magnetic fields of complex objects often exhibit the repeated breaking and rejoining of magnetic field lines. This is seen on the Sun for example, with spectacular releases of energy. Researchers believe that this could be the case for black holes too. The right magnetic interaction could accelerate particles away from the black hole, removing some of its energy.

"Black holes are commonly surrounded by a hot 'soup' of plasma particles that carry a magnetic field," Luca Comisso from Columbia University said in a statement. "Our theory shows that when magnetic field lines disconnect and reconnect, in just the right way, they can accelerate plasma particles to negative energies and large amounts of black hole energy can be extracted."

The sci-fi reason why this is exciting is that by getting energy from a black hole, you are getting a lot more energy out compared to the energy supplied. The team estimates that the process could have an efficiency of up to 150 percent, something that is unachievable on Earth. So an advanced alien civilization could decide to use a black hole as an incredible power station if it had the know-how.

The scientific reason it's exciting is that this process might already happen in nature, without the help of intelligent aliens. There are several phenomena surrounding black holes that are not fully understood, such as black hole flares that can be detected from Earth, so it is possible that magnetic reconnection in the ergosphere could help explain what we see.

"Our increased knowledge of how magnetic reconnection occurs in the vicinity of the black hole might be crucial for guiding our interpretation of current and future telescope observations of black holes, such as the ones by the Event Horizon Telescope," said co-author Felipe Asenjo from Universidad Adolfo Ibanez in Chile.

Perhaps in the future, mining energy from black holes could be the answer to our power needs.

"Thousands or millions of years from now, humanity might be able to survive around a black hole without harnessing energy from stars," Comisso said. "It is essentially a technological problem. If we look at the physics, there is nothing that prevents it."

## Black holes like giant balls of string, claims study

Research into what happens when objects fall into black holes may have reconciled two methods of understanding the universe.

Friday 27 July 2018 12:57, UK

A new scientific study to explain how black holes could exist has suggested that they are actually quite like giant balls of string.

Black holes are areas of space-time which are so dense that nothing can escape them - whether it is matter or energy.

But this raises a paradox between two methods of understanding the universe, quantum mechanics and general relativity.

Some physicists have attempted to answer this paradox by suggesting the existence of a burning "firewall" around the edge of black holes, which destroy any objects before they reach a black hole's surface.

But a team from Ohio State University has potentially disproved this by calculating what would happen if an electron fell into a black hole, in a paper published in the Journal of High Energy Physics.

Professor Samir Mathur said: "The probability of the electron hitting a photon from the radiation and burning up is negligible, dropping even further if one considers larger black holes known to exist in space.

"What we've shown in this new study is a flaw in the firewall argument," Professor Mathur added.

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After months of intense mathematical analysis, Professor Mathur and his team have established the figures challenging the firewall theory.

Their work uses string theory - a scientific model of the universe which considers everything to be composed of subatomic string-like tubes of energy.

String theory is a way to tie quantum mechanics (the mechanics of particles even smaller than atoms) and Albert Einstein's theory of relativity, which says that all objects fall the same way, despite their mass or composition.

Professor Mathur said he has always been sceptical of the firewall theory, preferring the model of black holes as balls of string, or fuzzballs.

"The question is, 'where does the black hole grab you?' We think that as a person approaches the horizon, the fuzzball surface grows to meet it before it has a chance to reach the hottest part of the radiation, and this is a crucial finding in this new physics paper that invalidates the firewall argument," he said.

"Once a person falling into the black hole is tangled up in strings, there's no easy way to decide what he will feel.

"The firewall argument had seemed like a quick way to prove that something falling through the horizon burns up.

"But we now see that there cannot be any such quick argument what happens can only be decided by detailed calculations in string theory," Professor Mathur added.

## Expository work Show abstracts Hide abstracts

A review of Quantum Ergodicity and related results, including a sketch of the proof of Quantum Ergodicity.

This is a broad review of recent developments related to the fractal uncertainty principle (unlike the previous review which focused in more detail on a single result).

These notes give a self-contained proof of the Stable/Unstable Manifold Theorem (also known as the Hadamard&ndashPerron Theorem) in hyperbolic dynamics. They also give two examples of hyperbolic systems: geodesic flows on negatively curved surfaces and dispersing billiards. The proof of the Stable/Unstable Manifold Theorem starts with a basic model case which however retains the essence of the general case. There are many figures throughout the text, and it is indended as a (somewhat) gentle introduction to some techniques in hyperbolic dynamics.

An expository article for the proceedings of Journées EDP (Roscoff, June 2017) describing the results and the proofs of previous works with Bourgain and Jin on fractal uncertainty principle and its application to control of eigenfunctions.

Lecture notes for lectures given at the Third Symposium on Scattering and Spectral Theory in Florianopolis, Brazil, July 2017 (work in progress).

Lecture notes for lectures given in Tsinghua University in Summer 2016.

Lecture notes for part of the course 18.158 given at MIT in Spring 2016.

A few movies demonstrating decay of correlations and equidistribution of velocities for billiards.

A demonstration of concentration in phase space (measured using the FBI transform) of various solutions to the damped wave equation on the circle with a potential.

Some (rather sloppy) notes for a (rather informal) talk on semiclassical Lagrangian distributions, Fourier integral operators, and their applications to quantization conditions given in March 2012.

This is a short introduction to nontrapping estimates in scattering theory. We discuss (1) how one can obtain exponential decay in obstacle scattering from a nontrapping estimate via the contour deformation argument (2) how to prove the semiclassical propagation of singularities estimate in the presence of a complex absorbing potential via Hörmander's positive commutator method (3) how propagation of singularities and complex scaling lead to a nontrapping estimate in the one-dimensional model case.

An article that served as the final project in Michael Hutchings' course on symplectic geometry in Spring 2009.

## JimsAstronomy

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-
--------------------- 1636 - What does Dark Matter Look Like?
-
- We don’t know it’s dark. Dark Matter is a discovery that needs more discovery. Astronomers see its gravitational effects, but, that is about as much as we know.

-. Dark Matter accounts for 5.4 times as much mass is ordinary manner in the universe. Ordinary matter is made of protons, neutrons, and electrons. We do not know what Dark Matter is made of, but, the math says it is out there made of something?

-. Ordinary matter in our galaxy is stars, gas, and dust in the structure of a giant disk. Our Milky Way is analogous to a warped vinyl record, 33 1/3 RPM.

-. The thin disk has a pin and wheel spiral pattern. In the center is a dense nucleus hosting a 4,500,000 Solar Mass blackhole. Through the center is in an elongated bulge known as a “bar“. Surrounding all of this is a “halo” of old stars.

-. Dark Matter’s structure is surmised from the gravitational effects on visible ordinary matter. Calculations tell us it is approximately spherical extending far beyond the halo. It's density falls off approximately as a square of the distance from the center the same as gravity does.
-
- At distances of 50,000 light-years from the center of our galaxy it consist mostly of atomic hydrogen and a few stars. By the time you get out 75,000 light-years distance the disc is warped bending 7,500 light-years out of the plane. The gas density is oscillating above and below the plane as it rotates around the center. These oscillations are 100 billion years in their cycle, completing one orbit about the center

-. At one point astronomers thought the neighboring galaxy, the Megellanic Cloud, was gravitationally causing this distortion. However, better measurements have determine thar the Megellanic gravity to be far too weak to have any effect.

-. In addition to the Megellanic Cloud galaxy there are 16 known satellite galaxies orbiting the Milky Way galaxy. Some of these dwarfs contain only a few hundred stars.

-. Could there be Dark Matter galaxies orbiting our galaxy? Could galaxy collisions early in the evolution of our galaxy cause the ringing that warps the shape of our galaxies disk? Could the center of gravity of Dark Matter be offset from the center of gravity of ordinary matter causing the asymmetry to occur? The puzzle of Dark Matter has become one of the most vibrant research areas in both physics and astronomy.
-
- Hydrogen gas emits a spectral line at the radio wavelength of 21 centimeters. Measuring the Doppler shift of this spectral line tells us relative velocities. With a little geometry a graph can be made showing the rotation velocity of stars, or galaxies, and their distances from the gravitational center.

-. Objects further from the center have further to travel and should be moving at faster speeds if the system is all held together. In contrast, the rotation curve for our solar system drops off with distance from the Sun, because inner planets orbit at faster speeds than the outer planets.

-. This is because the system’s mass is at the center, the Sun. The gravitational force holding a planet in orbit decreases as the inverse of the square of the distance from the Sun. A smaller force means lower orbital speed.

-. Our galaxy is different. Unlike the rotation curve for a solar system are galaxies orbital velocities remain constant beyond the inner thousand light-years which makes the rotation curve flat.
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- Unlike a solar system most of the mass of the galaxy must not be concentrated at the center. The orbits of progressively more distant objects must encircle more and more mass.

-. The Sun's orbit encompasses 100 billion Solar Mass. An orbit twice as large encompasses twice as much mass. Mathematical analysis implies that most of the mass is located in a spherical halo surrounding the disk of our galaxy. It must be 10 times the total mass in the galaxy disk. 90 percent of the total mass must be Dark Matter?

-. For example: a galaxy cluster has a radius of 6.2 million light-years. And an orbiting galaxy has a velocity of 1,350 kilometers per second, 3,019,864 miles per hour.
-
-
-------------------------- M = 4 * pi*a^3 / G * p^2
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-------------------------- v = 2 * pi* a / p
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-------------------------- M = r * v^2 / G
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-------------------------- M = 1.6*10^10 r * v^2
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- The mass is directly proportional to the radius times the velocity squared.
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-------------------------- M = 1.6 * 10^45 kilograms
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-------------------------- Solar Mass = 2 * 10^30 kilograms
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-------------------- M = 8*10^14 Solar Masses
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- The total mass is 800 trillion Solar Masses
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- One Milky Way mass is 1 trillion Solar Masses
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- The Galaxy Cluster is 800 Galaxy Masses
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-. Comparing the clusters mass to its luminosity determined the cluster's mass is made much, much, greater than the luminosity mass.

-. A second method to determine the clusters mass uses a temperature of X-ray hot gas. The gas temperature is related to the speed of the individual gas particles.
-
------------------ velocity = 140 meters / second * square root of Temperature
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------------------ The hot gas temperature of the cluster = 90,000,000 Kelvin
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------------------- v = 140 * (9*10^7)^½
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------------------- v = 1.3 * 10^6 meters per second
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------------------- M = 1.5 * 10^45 kilograms
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- The Galaxy Cluster is 800 Galaxy Masses, same answer.

-No cluster of galaxy galaxies contains enough visible matter to stay bound together. Galaxies orbit at velocities that should be flying apart. So what is holding them together? The total mass needed to bind a typical cluster is 10 times greater than the mass of the material that shows up in the visible light images.

## Here’s the first picture of a black hole

The first image of a black hole shows a bright ring with a dark, central spot. That ring is a bright disk of gas orbiting the supermassive behemoth in the galaxy M87. The spot is the black hole’s shadow.

Event Horizon Telescope Collaboration

This is what a black hole looks like.

A black hole isn’t really a hole. It’s an object in space with incredible mass packed into a very small area. All that mass creates such a huge gravitational tug that nothing can escape a black hole, including light.

#### Explainer: What are black holes?

The newly imaged supermassive monster lies in a galaxy called M87. A world-spanning network of observatories called the Event Horizon Telescope, or EHT, zoomed in on M87 to create this first-ever picture of a black hole.

“We have seen what we thought was unseeable,” Sheperd Doeleman said April 10 in Washington, D.C. “We have seen and taken a picture of a black hole,” he reported at one of seven concurrent news conferences. Doeleman is EHT’s director. He also is an astrophysicist at the Harvard-Smithsonian Center for Astrophysics in Cambridge, Mass. Results from his team’s work appear in six papers in the Astrophysical Journal Letters.

The concept of a black hole was first hinted at back in the 1780s. The mathematics behind them came from Albert Einstein’s 1915 general theory of relativity. And the phenomenon got its name “black hole” in the 1960s. But until now, all “pictures” of black holes have been illustrations or simulations.

#### “We’ve been studying black holes so long, sometimes it’s easy to forget that none of us have actually seen one.”

###### — France Córdova, director of the National Science Foundation

“We’ve been studying black holes so long, sometimes it’s easy to forget that none of us have actually seen one,” France Córdova said in the Washington, D.C., news conference. She is director of the National Science Foundation. Seeing a black hole “is a Herculean task,” she said.

That’s because black holes are famously hard to see. Their gravity is so extreme that nothing, not even light, can escape across the boundary at a black hole’s edge. That edge is known as the event horizon. But some black holes, especially supermassive ones dwelling in galaxies’ centers, stand out. They gather bright disks of gas and other material that surrounds the black hole. The EHT image reveals the shadow of M87’s black hole on its accretion disk. That disk looks like a fuzzy, asymmetrical ring. It unveils for the first time the dark abyss of one of the universe’s most mysterious objects.

“It’s been such a buildup,” Doeleman said. “It was just astonishment and wonder… to know that you’ve uncovered a part of the universe that was off limits to us.”

The much-anticipated big reveal of the image “lives up to the hype, that’s for sure,” says Priyamvada Natarajan. This astrophysicist at Yale University, in New Haven, Conn., is not on the EHT team. “It really brings home how fortunate we are as a species at this particular time, with the capacity of the human mind to comprehend the universe, to have built all the science and technology to make it happen.”

#### Einstein was right

The new image aligns with what physicists expected a black hole to look like based on the theory of general relativity by Albert Einstein. That theory predicts how spacetime is warped by the extreme mass of a black hole. The picture is “one more strong piece of evidence supporting the existence of black holes. And that, of course, helps verify general relativity,” says Clifford Will. He’s a physicist at the University of Florida in Gainesville, who is not on the EHT team. “Being able to actually see this shadow and to detect it is a tremendous first step.”

Studies in the past have tested general relativity by looking at the motions of stars or gas clouds near a black hole, but never at its edge. “It’s as good as it gets,” Will says. Tiptoe any closer and you’d be inside the black hole. And then you’d be unable to report back on the results of any experiments.

“Black hole environments are a likely place where general relativity would break down,” says EHT team member Feryal Özel. She is an astrophysicist who works at the University of Arizona in Tucson. So testing general relativity in such extreme conditions could reveal things that don’t seem to support Einstein’s predictions.

#### Explainer: Quantum is the world of the super small

However, she adds, just because this first image upholds general relativity “doesn’t mean general relativity is completely fine.” Many physicists think that general relativity won’t be the last word on gravity. That’s because it’s incompatible with another essential physics theory, quantum mechanics. This theory describes physics on very small scales.

The new image provided a new measurement of the size and heft of M87’s black hole. “Our mass determination by just directly looking at the shadow has helped resolve a longstanding controversy,” Sera Markoff said in the Washington, D.C., news conference. She’s a theoretical astrophysicist at the University of Amsterdam in the Netherlands. Estimates made using different techniques have ranged between 3.5 billion and 7.22 billion times the mass of the sun. New EHT measurements show that the mass of this black hole is about 6.5 billion solar masses.

The team also has figured out the behemoth’s size. Its diameter stretches 38 billion kilometers (24 billion miles). And the black hole spins clockwise. “M87 is a monster even by supermassive black hole standards,” Markoff said.

Scientists have been speculating for years about what a black hole would actually look like. Now, they finally know the answer.

EHT trained its sights on both M87’s black hole and Sagittarius A*. That second supermassive black hole sits at the center of our galaxy, the Milky Way. But, the scientists found it easier to image M87’s monster, even though it’s about 2,000 times as far away as Sgr A*.

M87’s black hole sits about 55 million light-years from Earth in the constellation Virgo. But it’s also about 1,000 times as massive as the Milky Way’s giant. Sgr A* only weighs the equivalent of roughly 4 million suns. M87’s extra heft nearly compensates for its greater distance. The size it covers in our sky “is pretty darn similar,” says EHT team member Özel.

Because M87’s black hole is bigger and has more gravity, gases swirling around it move and vary in brightness more slowly than they do around Sgr A*. And here’s why that’s important. “During a single observation, Sgr A* doesn’t sit still, whereas M87 does,” says Özel. “Just based on this ‘Does the black hole sit still and pose for me?’ point of view, we knew M87 would cooperate more.”

With more data analysis, the team hopes to solve some long-standing mysteries about black holes. These include how M87’s black hole spews such a bright jet of charged particles many thousands of light-years into space.

This first image is like the “shot heard round the world” that kicked off the American Revolutionary War, says Avi Loeb. He is an astrophysicist at Harvard University in Cambridge, Mass. “It’s very significant. It gives a glimpse of what the future might hold. But it doesn’t give us all the information that we want.”

The team does not yet have a picture of Sgr A*. But the researchers were able to collect some data on it. They are continuing to analyze those data in the hopes of adding to a new gallery of black hole portraits. Since the appearance of that black hole changes so quickly, the team is having to develop new techniques to analyze the data from it.

“The Milky Way is a very different galaxy from M87,” Loeb notes. Studying such different environments could reveal more details of how black holes behave, he says.

The next look at the M87 and Milky Way behemoths will have to wait, though. Scientists got a lucky stretch of good weather at all eight sites that made up the Event Horizon Telescope in 2017. Then there was bad weather in 2018. (Water vapor in the atmosphere can interfere with the telescope’s measurements.) Technical difficulties cancelled this year’s observing run.

The good news is that by 2020, EHT will include 11 observatories. The Greenland Telescope joined the consortium in 2018. The Kitt Peak National Observatory outside Tucson, Ariz., and the NOrthern Extended Millimeter Array (NOEMA) in the French Alps will join EHT in 2020.

Adding more telescopes should allow the team to extend the image. That would let EHT better capture the jets that spew from the black hole. The researchers also plan to make observations using light having a slightly higher frequency. That can further sharpen the image. And even bigger plans are on the horizon — adding telescopes that orbit Earth. “World domination is not enough for us. We also want to go to space,” Doeleman quipped.

These extra eyes may be just what’s needed to bring black holes into even greater focus.

Staff writer Maria Temming contributed to this story.

### Power Words

align (noun: alignment) To place or organize things in a patterned order, following an apparent line.

astrophysics An area of astronomy that deals with understanding the physical nature of stars and other objects in space. People who work in this field are known as astrophysicists.

behemoth A term for anything that is amazingly big. The term comes from a monstrous animal described in the Bible’s book of Job.

black hole A region of space having a gravitational field so intense that no matter or radiation (including light) can escape.

consortium A group or association of independent organizations.

constellation Patterns formed by prominent stars that lie close to each other in the night sky. Modern astronomers divide the sky into 88 constellations, 12 of which (known as the zodiac) lie along the sun’s path through the sky over the course of a year. Cancri, the original Greek name for the constellation Cancer, is one of those 12 zodiac constellations.

diameter The length of a straight line that runs through the center of a circle or spherical object, starting at the edge on one side and ending at the edge on the far side.

event horizon An imaginary sphere that surrounds a black hole. The more massive the black hole, the bigger the sphere. Anything that happens inside the event horizon is invisible, because gravity is so strong that under normal circumstances even light can’t escape. But according to some theories of physics, in certain situations small amounts of radiation can escape.

galaxy A massive group of stars bound together by gravity. Galaxies, which each typically include between 10 million and 100 trillion stars, also include clouds of gas, dust and the remnants of exploded stars.

gravity The force that attracts anything with mass, or bulk, toward any other thing with mass. The more mass that something has, the greater its gravity.

light-year The distance light travels in one year, about 9.48 trillion kilometers (almost 6 trillion miles). To get some idea of this length, imagine a rope long enough to wrap around the Earth. It would be a little over 40,000 kilometers (24,900 miles) long. Lay it out straight. Now lay another 236 million more that are the same length, end-to-end, right after the first. The total distance they now span would equal one light-year.

mass A number that shows how much an object resists speeding up and slowing down — basically a measure of how much matter that object is made from.

mechanics The study of how things move.

Milky Way The galaxy in which Earth’s solar system resides.

National Science Foundation The U.S. Congress created this independent federal agency in 1950 to promote the advancement of science national health, prosperity and welfare and the nation’s defense. This agency funds nearly one-fourth of all federally supported basic research in U.S. colleges and universities. In many fields such as mathematics, computer science and the social sciences, NSF is the major source of federal funding.

network A group of interconnected people or things. (v.) The act of connecting with other people who work in a given area or do similar thing (such as artists, business leaders or medical-support groups), often by going to gatherings where such people would be expected, and then chatting them up. (n. networking)

observatory (in astronomy) The building or structure (such as a satellite) that houses one or more telescopes.

particle A minute amount of something.

physics The scientific study of the nature and properties of matter and energy. Classical physics is an explanation of the nature and properties of matter and energy that relies on descriptions such as Newton’s laws of motion. Quantum physics, a field of study that emerged later, is a more accurate way of explaining the motions and behavior of matter. A scientist who works in such areas is known as a physicist.

quantum (pl. quanta) A term that refers to the smallest amount of anything, especially of energy or subatomic mass.

quantum mechanics A branch of physics dealing with the behavior of matter on the scale of atoms or subatomic particles.

relativity (in physics) A theory developed by physicist Albert Einstein showing that neither space nor time are constant, but instead affected by one’s velocity and the mass of things in your vicinity.

spacetime A term made essential by Einstein’s theory of relativity, it describes a designation for some spot given in terms of its three-dimensional coordinates in space, along with a fourth coordinate corresponding to time.

standards (in research) The values or materials used as benchmarks against which other things can be compared.

star The basic building block from which galaxies are made. Stars develop when gravity compacts clouds of gas. When they become dense enough to sustain nuclear-fusion reactions, stars will emit light and sometimes other forms of electromagnetic radiation. The sun is our closest star.

sun The star at the center of Earth’s solar system. It’s an average size star about 26,000 light-years from the center of the Milky Way galaxy. Also a term for any sunlike star.

telescope Usually a light-collecting instrument that makes distant objects appear nearer through the use of lenses or a combination of curved mirrors and lenses. Some, however, collect radio emissions (energy from a different portion of the electromagnetic spectrum) through a network of antennas.

theoretical An adjective for an analysis or assessment of something that based on pre-existing knowledge of how things behave. It is not based on experimental trials. Theoretical research tends to use math — usually performed by computers — to predict how or what will occur for some specified series of conditions. Experimental testing or observations of natural systems will then be needed to confirm what had been predicted.

theory (in science) A description of some aspect of the natural world based on extensive observations, tests and reason. A theory can also be a way of organizing a broad body of knowledge that applies in a broad range of circumstances to explain what will happen. Unlike the common definition of theory, a theory in science is not just a hunch. Ideas or conclusions that are based on a theory — and not yet on firm data or observations — are referred to as theoretical. Scientists who use mathematics and/or existing data to project what might happen in new situations are known as theorists.

universe The entire cosmos: All things that exist throughout space and time. It has been expanding since its formation during an event known as the Big Bang, some 13.8 billion years ago (give or take a few hundred million years).

verify (n. verification) To demonstrate or confirm in some way that a particular claim or suspicion is true.

weather Conditions in the atmosphere at a localized place and a particular time. It is usually described in terms of particular features, such as air pressure, humidity, moisture, any precipitation (rain, snow or ice), temperature and wind speed. Weather constitutes the actual conditions that occur at any time and place. It’s different from climate, which is a description of the conditions that tend to occur in some general region during a particular month or season.

### Citations

Journal: The Event Horizon Telescope Collaboration et al. First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole. The Astrophysical Journal Letters. Published online April 10, 2019. doi:10.3847/2041-8213/ab0cc7.

Journal: The Event Horizon Telescope Collaboration et al. First M87 Event Horizon Telescope Results. II. Array and Instrumentation. The Astrophysical Journal Letters. Published online April 10, 2019. doi:10.3847/2041-8213/ab0c96.

Journal: The Event Horizon Telescope Collaboration et al. First M87 Event Horizon Telescope Results. III. Data Processing and Calibration. The Astrophysical Journal Letters. Published online April 10, 2019. doi:10.3847/2041-8213/ab0c57.

Journal: The Event Horizon Telescope Collaboration et al. First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole. The Astrophysical Journal Letters. Published online April 10, 2019. doi:10.3847/2041-8213/ab0e85.

Journal: The Event Horizon Telescope Collaboration et al. First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring. The Astrophysical Journal Letters. Published online April 10, 2019. doi:10.3847/2041-8213/ab0f43.

Journal: The Event Horizon Telescope Collaboration et al. First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole. The Astrophysical Journal Letters. Published online April 10, 2019. doi:10.3847/2041-8213/ab1141.

Lisa Grossman is the astronomy writer. She has a degree in astronomy from Cornell University and a graduate certificate in science writing from University of California, Santa Cruz. She lives near Boston.

Physics writer Emily Conover studied physics at the University of Chicago. She loves physics for its ability to reveal the secret rules about how stuff works, from tiny atoms to the vast cosmos.

## Black-hole breakthrough: New images show magnetic fields around M87*

The black hole at the centre of the M87 galaxy is like a giant fire-breathing dragon that spews enormous jets of energetic particles at near light speeds across some 5,000 light years of space.

A new view of this black hole in polarized light, released today by the Event Horizon Telescope (EHT) collaboration, will help astrophysicists understand just how those jets are launched by this monstrous black hole.

A team led by Avery Broderick, a member of the EHT collaboration who is an astrophysicist at the University of Waterloo and Perimeter Institute for Theoretical Physics in Waterloo, contributed to making this new view in polarized light possible.

“It is a breakthrough in radio astronomy to see the polarization structure on horizon scales around the black hole,” Broderick said.

The black hole known as M87* (for Messier 87 star) became famous in 2019 as the subject of the historic first-ever picture of a black hole ever taken.

This is yet another first. It is the first time that astronomers have been able to measure polarization this close to the edge of a black hole. It enables scientists to trace the structure of the magnetic fields that drive the powerful jets extending far beyond the galaxy.

In the same way polarised sunglasses help us see better by reducing reflections and glare from bright surfaces, astronomers can sharpen their vision of the region around the black hole by looking at how the light originating from there is polarized.

“The observations suggest that the magnetic fields at the black hole’s edge are strong enough to push back on the hot gas and help it resist gravity’s pull. Only the gas that slips through the field can spiral inwards to the event horizon,” said Jason Dexter, Assistant Professor at the University of Colorado Boulder, US, and one of the co-ordinators of the EHT Theory Working Group, in a press release.

But getting accurate polarization data has been a long-standing challenge in radio astronomy. Broderick and his team played a part in finding solutions to those problems.

“Misaligned antennas, imperfect polarization signal separation, and wavelength-dependent optical elements all result in mixing polarized and unpolarized emission — this mixing has the unfortunate effect of creating false polarization signals and corrupting real ones,” Broderick said.

One was the development of Themis, the flexible and powerful analysis software that helps extract information from the observational data much more efficiently, and thus improves the accuracy in modelling the physical processes around black holes.

“Themis is a suite of analysis tools. It's really an analysis framework for EHT data and it was a key component in the first M87 science results. But now, it's also expanded polarized image production,” Broderick says.

It helps the telescopes work “smarter, not harder,” Broderick says. It is also modular and can be adapted to fit new data sets over time, Broderick adds. “It's a LEGO set for building analysis of EHT data.”

Broderick also worked with collaborators to develop “closure traces,” a clever mathematical way of combining multiple telescope measurements in order to circumvent polarization errors.

They drew inspiration from the work of radio astronomers in the late 1950s, who developed other types of “closure quantities” to correct for errors in the phase and amplitude measurements of the light coming into telescopes. “Closure traces are the first such quantities discovered in 60 years, and provide a direct window onto the polarized structure of M87,” Broderick says.

Broderick was also central to bringing the EHT’s new view into agreement with that from ALMA (the Atacama Large Millimeter/submillimeter Array) in northern Chile, on scales a million times larger. This was done by simultaneously modeling the small-scale structures seen by the EHT and a large-scale component seen only by ALMA, placing limits on a key systematic uncertainty—Faraday rotation—that bedevils the interpretation of astronomical polarization generally.

The new polarized light images of M87* is a tremendous achievement, Broderick said. No longer are scientists merely looking at “blobs of light” moving in a halo around a black hole. “Now we’re studying actual structures.”

The jets launched by supermassive black holes have an enormous impact on the formation and structure of galaxies and clusters of galaxies, he adds. “If you wanted to understand why galaxies and galaxy clusters look the way they do, you absolutely have to understand how black holes do this magic trick.”

Seeing how black holes interact with their surroundings can also help inform physicists about gravity in extreme environments. Over time, it will also help them “build out the dictionary” to relate the astronomical measurements taken now and in the past, to what black holes are doing.

In a sense, M87 and how it launches its jets can be like a “Rosetta Stone” in understanding the cosmos, Broderick says. The jets launched by black holes shape their environment on intergalactic scales, expanding the influence of the black hole well beyond its immediate vicinity. “Every piece of evidence that tells us a little bit more about where these jets come from is settling key questions in why the universe looks the way it does.”