black holes – One Universe at a Time https://briankoberlein.com Brian Koberlein Thu, 21 Feb 2019 22:09:36 +0000 en-US hourly 1 https://wordpress.org/?v=5.1 The Black Hole At The Edge Of The Universe https://briankoberlein.com/2017/12/12/black-hole-edge-universe/ https://briankoberlein.com/2017/12/12/black-hole-edge-universe/#comments Tue, 12 Dec 2017 12:00:36 +0000 https://briankoberlein.com/?p=6809

The most distant quasar ever observed challenges our understanding of how black holes formed.

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Within most galaxies there lurks a supermassive black hole. Our own galaxy, for example contains a black hole 4 million times more massive than our Sun. One of the big mysteries of these black holes is just how they formed, and how long it took for them to reach such a massive size. Now a massive black hole at the edge of the observable universe challenges our understanding of them. 

We discovered this distant black hole because it is a quasar. When a black hole captures nearby material, the material becomes superheated and radiates powerful radio energy and x-rays. These beacons of light are so bright they can only be powered by supermassive black holes. By observing the brightness of distant quasar we can calculate the mass of its black hole engine.

Recently astronomers discovered the most distant quasar ever. Known as J1342+0928, it is so distant we see it from a time when the universe was only 690 million years old. At that time galaxies were just starting to form. But this quasar gives off so much light that its black hole must be 800 million times the mass of our Sun. So how did this particular black hole get so massive so soon? It’s possible that it exists in a rather dense region of space. Having lots of matter around would make it easier to grow quickly. But that isn’t enough to solve the mystery, because the faster a black hole consumes matter, the more light the matter would emit, and that pressure of light and heat would tend to push matter away from the black hole. It’s known as the Eddington limit, and it puts an upper bound on how fast a black hole can grow. To reach 800 million solar masses in such a short time, the black hole would have to consume matter fairly close to this limit.

The big question about this black hole is whether it is simply an unusually early bloomer, or if it is rather typical of black holes in the early universe. To answer that question we will need to find more examples of large quasars on the edge of the cosmos. So the race is on to find these most distant of beacons. If we can find them, they will help us understand how supermassive black holes and their galaxies formed.

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Black Hole Dance https://briankoberlein.com/2017/07/05/black-hole-dance/ https://briankoberlein.com/2017/07/05/black-hole-dance/#comments Wed, 05 Jul 2017 11:00:33 +0000 https://briankoberlein.com/?p=6687

The VLBA has observed two supermassive black holes orbiting each other in a gravitational dance.

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At the heart of most galaxies is a supermassive black hole. These powerhouses have a mass of millions or billions of Suns, and can create brilliant quasars when active. So what happens when two galaxies collide?

According to the models, when galaxies collide and merge, their two black holes capture each other in an orbital dance. Over time the black holes would spiral ever closer, eventually merging into a single black hole. We have seen smaller black holes merge through the gravitational waves they produce, but supermassive black holes mergers are rare, so we haven’t seen their gravitational waves. But if our models are correct, many galaxies should contain a binary black hole. The challenge is seeing them.

VLBA image of the central region of the galaxy 0402+379, showing the two cores, labeled C1 and C2, identified as a pair of supermassive black holes in orbit around each other.
Credit: Bansal et al., NRAO/AUI/NSF.

We have seen a few cases of binary supermassive black holes, but these are largely through indirect evidence. Seeing two black holes close together and proving they orbit each other takes careful observation over time. In 2009 a collection of radio telescopes across the world known as the Very Long Baseline Array (VLBA) observed two supermassive black holes that appeared to be close together. They appeared to be located in an elliptical galaxy known as 0402+379, making them an orbiting binary. But it was also possible that the two were a visual binary. That is, from Earth they could appear to be close together, but in reality one of the black holes could be much more distant.

To prove they orbit each other, VLBA made another set of observations in 2015. The positions of the black holes had shifted, which confirmed they were orbiting each other. To determine their orbit, the team also used VLBA data gathered in 2003. From the positions of these black holes over the course of more than a decade, they found they orbit each other with a period of about 30,000 years. They are only about 24 light years apart, and their combined mass is about 15 billion Suns.

Paper: K. Bansal et al. Constraining the Orbit of the Supermassive Black Hole Binary 0402+379. The Astrophysical Journal (2017). DOI: 10.3847/1538-4357/aa74e1

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Looking At The Void https://briankoberlein.com/2017/04/10/looking-at-the-void/ https://briankoberlein.com/2017/04/10/looking-at-the-void/#comments Mon, 10 Apr 2017 11:00:05 +0000 https://briankoberlein.com/?p=6596

We've never observed a black hole directly, but that could change soon.

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Astronomers have never observed a black hole directly. We know they exist. We can see the powerful jets produced by active supermassive black holes. We can see stars orbiting the black hole in the center of the Milky Way. We can also observe the gravitational waves produced when two black holes merge. What we haven’t observed is the region just outside a black hole’s event horizon. But the Event Horizon Telescope is now trying to do just that. 

Participating observatories of the Event Horizon Telescope (EHT) and the Global mm-VLBI Array (GMVA). Credit: ESO/O. Furtak

The Event Horizon Telescope (EHT) isn’t a single telescope, but rather a collection of radio telescopes working together from all over the world. Each will observe the center of our galaxy at a wavelength of about 1.3 millimeters. This wavelength was chosen because it is a wavelength where the gas and dust surrounding the center of our galaxy is relatively transparent.

But the greatest challenge to observing a black hole is its size. The center of our galaxy is 26,000 light years way, and while the supermassive black hole it contains has a mass of about 4 million Suns, it is only 20 times wider than the Sun. To see the region around such a small object requires an extremely high resolution telescope. More than a single radio telescope can provide. But by combining observations from telescopes all over the world, we can create a “virtual telescope” the size of Earth itself. In this way we can get a resolution down to about 50 microarcseconds.

If the project is successful, it will give us a direct view of the region around a black hole, and this will allow us to test whether our understanding of black holes is correct. For example, the light coming from just outside the black hole should be caused by synchrotron radiation, so it will be highly polarized. According to general relativity, the warped space around the black hole will twist the polarized light in ways we can measure. By observing the gravitational effect on light, we can test whether general relativity is correct.

What’s perhaps most amazing about this project is that it is perhaps the largest collaborative astronomy project we’ve ever undertaken. Countries from from all over the world have come together, all to try to observe one of the smallest objects in our galaxy.

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How To Get Rid Of A Black Hole https://briankoberlein.com/2017/04/05/get-rid-black-hole/ https://briankoberlein.com/2017/04/05/get-rid-black-hole/#comments Wed, 05 Apr 2017 11:00:52 +0000 https://briankoberlein.com/?p=6579

How does a galaxy get rid of a supermassive black hole?

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Most galaxies like our Milky Way have a supermassive black hole in their core. They can have more mass than millions or billions of Suns. But there are a few spiral galaxies, such as the Triangulum galaxy, that has no supermassive black hole. Given that supermassive black holes form within galaxies, how could a galaxy possibly get rid of one? The answer could be gravitational waves. 

Every now and then two galaxies can collide and merge. For example, the Andromeda galaxy and Milky Way are moving toward each other, and will collide in about 4 billion years. When two galaxies collide, their supermassive black holes can be caught in a spiral toward each other. As they orbit each other, their large masses produce strong gravitational waves, which eventually causes them to merge.

A diagram showing how two merging black holes can be ejected from a galaxy. Credit: NASA, ESA/Hubble, and A. Feild/STScI

We’ve observed the gravitational waves of merging black holes, but the gravitational waves of supermassive black holes would be much stronger. If the two merging black holes are roughly the same size, then the gravitational waves would be generated evenly in a range of directions. But if the black holes have very different sizes, then gravitational waves would be produced more strongly in one direction than others. This means more gravitational energy is being emitted in a particular direction, and as a result the black holes would be kicked in the opposite direction. This could be strong enough to kick a supermassive black hole out of the merged galaxy.

At least that’s been one idea, and new observational evidence seems to support it. A team using the Hubble space telescope have found a supermassive black hole moving away from a galaxy. You can see this as the bright object in the center of image at the top of the page. The black hole is bright because it’s actively consuming gas and dust. Behind the black hole is the fainter and diffuse galaxy 3C186. Given the structure of 3C186, it is most likely the result of two merged galaxies. This is exactly what we’d expect to see when merging black holes are kicked out of a galaxy.

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Supermassive Black Holes Can Trigger Star Formation https://briankoberlein.com/2017/04/03/supermassive-black-holes-can-trigger-star-formation/ https://briankoberlein.com/2017/04/03/supermassive-black-holes-can-trigger-star-formation/#comments Mon, 03 Apr 2017 11:00:46 +0000 https://briankoberlein.com/?p=6564

Supermassive black holes lurk in the hearts of galaxies, and they can trigger the formation of new stars.

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Stars typically form where there is a large buildup of gas and dust, known as a stellar nursery. But new observations show that star formation can also be triggered by a supermassive black hole in the center of a galaxy. 

Most galaxies contain a supermassive black hole within them. These black holes can have masses of millions or even billions of Suns. Their immense gravity can not only rip stars apart, they can generate powerful outflows of material (or jets) as they are active. These outflows are a rich source of gas and dust that can trigger the formation of new stars.

While it has been speculated that stars could form from these outflows, the process is difficult to observe. But recently a team of astronomers observed a pair of colliding galaxies about 600 million light years away. Because of their collision, their supermassive black hole is extremely active, and producing a large outflow of material. Using sensitive spectroscopic measurements, the team was able to detect stars forming within the outflow. These stars were hotter and brighter than stars usually found in stellar nurseries, and their observed speeds were consistent with that of the outflow.

This discovery helps us understand the evolution of both stars and galaxies. Since supermassive black holes can trigger the formation of large, bright stars, these stars could provide the heavy elements necessary for the formation of Sun-like stars and metal-rich planets. It provides another avenue for star production within a young galaxy.

Paper: R. Maiolino, et al. Star Formation in a Galactic Outflow. Nature (2017)

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Black Holes And Dark Matter https://briankoberlein.com/2017/04/01/black-holes-dark-matter/ https://briankoberlein.com/2017/04/01/black-holes-dark-matter/#comments Sat, 01 Apr 2017 11:00:42 +0000 https://briankoberlein.com/?p=6567

We haven't completely ruled out black holes as the source of dark matter, but there are few mass ranges left.

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Over the years, dark matter has remained an enigma. Observations of things like large scale galaxy distribution and the motion of stars and gas within galaxies points to the existence of some sort of weakly interacting matter, we still haven’t figured out what this dark matter could be. We know a lot of things it can’t be, such as neutrinos, but the solution still eludes us. So one idea that keeps coming back is that dark matter might be due to black holes. Not stellar mass black holes formed from dying stars, or supermassive black holes found in the centers of galaxies, but smaller black holes that may have formed in the early universe. 

The idea that small black holes could be dark matter is a pretty good one. Small black holes could be widely distributed, giving the halo effect we see around galaxies. Their small size would mean they wouldn’t absorb much light (making them “dark” in astronomical terms). Plus, the idea doesn’t need to call upon any kind of exotic yet to be seen type of matter. Small, primordial black holes could have formed from regular matter during the early moments of the big bang.

Observational constraints on dark matter black holes.

It’s also a theory we can test, and that’s where the idea starts to fall apart. Dark matter comprises the majority of mass within galaxies, so if it was comprised of small black holes, there would have to be a lot of them. If these black holes were fairly large (say, on the order of a solar mass or more) then we should observe them distort starlight that they pass in front of though an effect known as gravitational microlensing. We’ve watched a lot of stars over time, and there has been no microlensing. If they were small black holes (about the mass of a moon) then there would be so many of them that they would distort the light from gamma ray bursts, and again we haven’t seen any evidence of that. If the black holes were really tiny, then Hawking radiation would have caused them to evaporate away long before now.

So most sizes of black holes have been ruled out as a possibility, but not all. If these primordial black holes were around the mass of a few Jupiters, then they would be too small to be observed through microlensing, but too large to have an effect on things like gamma ray bursts. As it stands, we don’t have an observational test that can rule out dark matter black holes with a narrow range of masses. Of course that would raise the question about why primordial black holes would only be in this mass range and not others. The good news is that with the dawn of gravitational astronomy we should be able to test the idea further in the future. If dark matter is comprised of Jupiter-mass black holes, then some of them will merge and create gravitational waves. Either we will see these waves eventually, or we will basically rule out black holes as an option for dark matter.

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Life In A Black Hole https://briankoberlein.com/2017/02/19/life-black-hole/ https://briankoberlein.com/2017/02/19/life-black-hole/#comments Sun, 19 Feb 2017 18:51:52 +0000 https://briankoberlein.com/?p=6482

What happens when you fall into a black hole? Maybe you could live a long and happy life.

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Your spacecraft is failing, and ahead looms the dark majesty of a black hole. As its gravity pulls you ever closer, you cross its event horizon and your fate is sealed. You are trapped forever. What happens next is the subject of numerous movies. Do you travel through a wormhole and enter another universe? Do you confront the intersection of reason and faith? Do you travel back in time to communicate with your daughter? The scientific answer is much more mundane. You die, crushed by the the tidal forces of the black hole interior as you are pulled inevitably to its singularity. But perhaps there is an alternative where you are trapped but could continue to live a full life. 

There is no question that if you enter a black hole you can never leave. The event horizon of a black hole ensures that not even light can escape a black hole. To find out what happens next, you have to calculate your orbital path within the black hole, what is known as a geodesic. The simplest geodesic to calculate is for a simple mass dropped into a non-rotating black hole. What is tells us is that you are fated to be crushed by the black hole singularity in a relatively short time. In a supermassive black hole you would have a bit more time, but your days are numbered. More general calculations support this idea. In relativity, the harder you try to escape, the more energy you would need, and the gravitational pull of that energy would work against you. Entering a non-rotating black hole is a death sentence.

Calculated orbits of light and matter near a singularity. Credit: Vyacheslav I. Dokuchaev

But real black holes rotate, and this is where things get more complicated. When a black hole rotates space and time are twisted through an effect known as frame dragging. Fall into a rotating black hole, and its rotation will cause you to spiral around the black hole as you’re entering it. Calculating the geodesics for a rotating black hole interior are more complex, and have to be done numerically. But given the way black holes work it was generally thought that rotation wouldn’t save you. You might orbit the singularity a few times before reaching it, but you would still be doomed. Recently, however, it was found that this might not be the case.

Calculations of orbital paths within rotating and charged black holes shows that it is possible to have stable orbits within a black hole’s event horizon. This means it would be possible to enter a black hole and find a stable orbit around the singularity. You’d still be trapped inside the black hole forever, but you wouldn’t be doomed. In principle, you could survive inside a black hole.

The calculations are only for the ideal case of orbits in a vacuum. Any radiation in the black hole, or other infalling matter would degrade your orbit and make it unstable, so you would still be doomed inside a real black hole. But perhaps with a bit of ingenuity and luck you might be able to create a somewhat stable orbit in order to live our your life before you reach a singularity grave. It’s all pretty speculative, but at the very least it gives science fiction an answer to “what happens next?” that is a bit closer to reality.

Paper: Vyacheslav I. Dokuchaev. Is there life inside black holes? Class. Quantum Grav. 28 235015 (2011)

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Deep Field Black Holes https://briankoberlein.com/2017/01/07/deep-field-black-holes/ https://briankoberlein.com/2017/01/07/deep-field-black-holes/#comments Sat, 07 Jan 2017 17:20:34 +0000 https://briankoberlein.com/?p=6426

A new x-ray deep field image supports the idea that supermassive black holes formed before galaxies did.

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At the heart of most galaxies lies a supermassive black hole. How such black holes came to be is a matter of some debate. Did black holes form first, and galaxies later formed around them (bottom up model), or did galaxies form first, and only later did their cores collapse into a black hole (top down model). To answer this question we need to have a good understanding of when these black holes started to form. A new ultra-deep x-ray image is helping to answer these questions.

A deep field image is one that has a clear view of very distant objects. The most famous deep field is the Hubble Ultra Deep Field (HUDF), which showed us just how many galaxies there are in the cosmos. The HUDF was in the visible and infrared, but there are others such as the ALMA Deep Field, which was taken at microwave wavelengths, which gave us a view of distant gas and dust. Now the Chandra X-ray Observatory has taken an x-ray deep field, which gives us a view of distant black holes.

Black holes don’t emit light themselves, but the gas and dust near a black hole can become superheated by the gravitational squeezing of the black hole. Such “active” black holes can emit huge jets of plasma that give off intense x-rays. By studying these x-ray emissions, we can determine things such as the size and rate of growth of the black hole. This new deep field image gathered light from supermassive black holes when the Universe was about 2 billion years old. Since the region observed was the same as the Hubble Deep Field, the team could match x-ray black holes to galaxies in the Hubble deep field, and get an idea of the size and evolution of the black holes and their galaxies. What they found was that the “seeds” for these supermassive black holes were likely on the order of 10,000 to 100,000 times more massive than our Sun. This would tend to support the bottom up model where black holes formed first. If the top down model was correct, we would assume the seeds would be smaller, on the order of 100 t0 1,000 solar masses.

This new data doesn’t completely rule out the top down model, but it is consistent with other evidence that supports the bottom up model. Right now it looks like black holes formed early in the Universe, and this triggered the formation of galaxies around them.

Paper: Fabio Vito, et al. The deepest X-ray view of high-redshift galaxies: constraints on low-rate black-hole accretion. MNRAS 463 (1): 348-374. doi: 10.1093/mnras/stw1998 (2016)

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Black Holes, Bright Lights https://briankoberlein.com/2016/12/13/black-holes-bright-lights/ https://briankoberlein.com/2016/12/13/black-holes-bright-lights/#respond Tue, 13 Dec 2016 16:34:08 +0000 https://briankoberlein.com/?p=6375

The brightest supernova observed may have been caused by a hungry black hole.

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Supernovae are the bright, but short lived explosions of a dying star. At their brightest they can outshine an entire galaxy. The brightest ones, known as superluminous supernovae, can be more than 10 times brighter than type Ia supernovae used to measure the distances of far galaxies. But there’s a limit to how bright a supernova can be, so when we observed a supernova last year that seemed to exceed that limit, it raised an interesting question. Is our model of superluminous supernovae wrong, or is something else going on? 

After the supernovae ASASSN-15lh reached its peak brightness, a team of astronomers observed the source for the next 10 months. They found that the way in which the supernova dimmed over time (known as its light curve) didn’t agree well with the light curves of other supernovae. This would imply the event was not caused by the explosion of an old star. Add too this the fact that supernovae generally occur where there are plenty of bright blue stars (since they tend to die as supernovae) and ASASSN-15lh occurred in a galaxy that mostly consists of smaller, redder stars.

One thing the team did see was that the supernovae got much brighter in the ultraviolet a while after the initial event. This is likely due to a reheating of the stellar material. That isn’t expected to happen in a supernovae event, but it can happen when a star is ripped apart by a black hole. So the team compared the data to models of star-eating black holes. They found that the best math for the data is a rapidly rotating black hole that ripped apart a small star. This doesn’t guarantee that the event really was a black hole’s lunch, but it points to the idea that some supernovae might not be stellar explosions after all.

We will still need more observations of superluminous supernovae to confirm this model, but it’s certainly likely given the gravitational power of black holes.

Paper: M. Fraser, et al. The superluminous transient ASASSN-15lh as a tidal disruption event from a Kerr black hole. Nature Astronomy 1 (2016) DOI:10.1038/s41550-016-0002

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Echoes From The Abyss https://briankoberlein.com/2016/12/03/echoes-from-the-abyss/ https://briankoberlein.com/2016/12/03/echoes-from-the-abyss/#comments Sat, 03 Dec 2016 20:00:50 +0000 https://briankoberlein.com/?p=6360

Observations of gravitational waves might allow us to test the quantum properties of black holes.

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With the detection of gravitational waves, we’re now able to observe black holes as they merge. We’re already able to determine the mass and rotation of the merging black holes, but gravitational waves might be able to settle the fierce debates over the conflict between black holes and quantum gravity. 

The signal of a classic black hole merger. Credit: LIGO

The signal of a classic black hole merger. Credit: LIGO

The LIGO signals we have so far show the classic properties of a black hole merger. Two orbiting black holes create a regular pattern of gravitational waves that gradually increase in frequency. Eventually the two masses merge, creating a chirp and “ringdown” as the newly formed black hole settles into a stable state. According to general relativity, once the new black hole settles down, it should no longer emit gravitational waves. That’s because a single black hole simply has the properties of mass and rotation (and theoretically charge), but nothing else. This is known as the “no-hair theorem.”

While relativity is a well-tested scientific theory, it runs into problems when you try to incorporate it into quantum theory. The foundational principles of quantum mechanics are very different from that of general relativity, so the two models don’t play well together. Since we have reasons to presume the ultimate theory of gravity is a quantum theory, there has been a lot of research on what such a theory would look like. When we try to develop a quantum version of black holes, weird paradoxes arise. One of them is known as the firewall paradox, where quantum fluctuations would create intense heat near the event horizon of a black hole, though this would seem to violate the equivalence principle, upon which relativity is based. Another is the information paradox, where knowledge of an object disappears when it crosses the event horizon, which violates a fundamental principle of quantum theory. Theorists have developed possible resolutions to these paradoxes, but there hasn’t been any way to test them. We can’t travel to a black hole to look at one up close.

Secondary echoes could be evidence of quantum effects. Credit: Jahed Abedi, et al.

Secondary echoes could be evidence of quantum effects. Credit: Jahed Abedi, et al.

But a new paper argues that LIGO might actually be able to test these ideas. While a classical black hole should be silent after the merger, quantum interactions near the event horizon could create small secondary chirps. These chirps should be regularly spaced, and their timing could put constraints on various quantum models. Interestingly, the team looked at data from the three black hole mergers that have been publicly announced, and found some evidence of these secondary signals. The statistics isn’t particularly strong, so it can’t be confirmed as a real effect, but that will change as we observe more black hole mergers. If these secondary chirps keep showing up, then we might be able to test the quantum behavior of black holes.

It’s an interesting result, and it demonstrates the power of gravitational astronomy.

Paper: Jahed Abedi, et al. Echoes from the Abyss: Evidence for Planck-scale structure at black hole horizonsarXiv:1612.00266 [gr-qc] (2016)

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Close Enough https://briankoberlein.com/2016/11/07/close-enough/ https://briankoberlein.com/2016/11/07/close-enough/#comments Mon, 07 Nov 2016 12:00:02 +0000 https://briankoberlein.com/?p=6339

To make a black hole, do we have to squeeze mass all the way to its limit, or do we just have to get close enough?

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A black hole is an object that has gravitationally collapsed under its own weight. It could be formed from the the remains of a dead star, a dense central region of a galaxy, or perhaps even a small fluctuation in the early dense moments of the cosmos. Regardless of the cause, the trick is to compress a large enough mass into a small enough volume. In other words, if the density of matter is high enough, it will collapse into a black hole.

The critical volume for a given mass, known as the Schwarzschild radius is pretty easy to calculate for a non-rotating black hole. It turns out to be R = 2GM/c2, where G is Newton’s gravitational constant, c is the speed of light, and M is the mass. Compress the mass into a sphere of that radius, and you get a black hole. At least that’s how the story is told. Technically, if you compress a mass into a sphere of that volume, then it already is a black hole. But is there a minimum volume you could reach so that the mass is fated to become a black hole? Do you have to actively squeeze the mass all the way to a black hole, or can you squeeze it to a point and let nature takes its course?

This turns out to be a very interesting question. If we simply compress a certain amount of matter into an ever smaller volume, the matter itself will try to push back. As matter is squeezed, it heats up, so eventually our matter would heat to the point of vaporizing, and the gas pressure would try to oppose us. Squeeze hard enough and the nuclei of the material will start fusing, which would heat the mass further and generate more pressure. Squeeze even harder and the matter will eventually reach a point where the electrons of the material are moving at nearly the speed of light, and the quantum pressure of electrons will push against you. This is what happens within a white dwarf star. But there’s a limit to how strongly electron pressure can push back, known as the Chandrasekhar limit. If we squeeze matter harder than that, the electrons and nuclei of the material will collapse together, forming a sea of neutrons.

Since fast moving neutrons occupy less space than fast moving electrons, for a time the mass gets easier to compress. But eventually the neutrons start approaching the speed of light, and push against each other in much the same way as the electrons did. This neutron pressure is what keeps neutron stars from collapsing on themselves. As with electrons, there’s a limit to how strongly neutrons can push back, known as the Tolman-Oppenheimer-Volkoff (TOV) limit. Squeeze the mass beyond that limit, and the neutrons will collapse into each other.

According to our current understanding of physics, beyond the TOV limit the matter will collapse into a black hole. The observed upper mass of neutron stars is about twice the mass of our Sun. Such neutron stars are about 20 kilometers in diameter, while the Schwarzschild radius for such a mass is about 6 kilometers. This would imply that if we squeezed mass into a radius about 1.7 times larger than the Schwarzschild radius, then it’s doomed to become a black hole.

But what if the TOV limit isn’t the last line of defense against a black hole? What if the quarks that make up protons and neutrons behave in ways we don’t expect at really high densities, or what if quarks are comprised of something even more fundamental, and they have an even stronger limit. It is possible that something could oppose our squeezing? Could such it create so much pressure that a black hole is impossible to form?

It turns out the answer is no, and the reason is because of relativity. One of the key aspects of relativity is that energy and mass are related. Mass can be converted into energy, and energy can be converted into mass. When matter generates pressure to oppose our squeezing, that pressure has a certain energy, and that energy has a gravitational weight just like mass. So the more strongly matter pushes against us, the more gravity helps us. This is a game of diminishing returns, and there is a point where no matter how strongly the mass opposes us, gravity is even stronger. This limit is known as the Buchdahl limit. If the mass is spherical and of uniform density, this limit is 9/8 times the Schwarzschild radius. Squeeze past that point, and nothing can oppose the eventual formation of a black hole. There are more general calculations that don’t assume uniform density, but the end result is similar. So it turns out we don’t have to squeeze a ball of mass all the way to its Schwarzschild radius to make a black hole. We just have to get within about 10% of the radius the mass will collapse into a black hole on its own.

While this is a fun theoretical game, it is an excellent example of why black holes exist.

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Are You A Black Hole? https://briankoberlein.com/2016/06/26/are-you-a-black-hole/ https://briankoberlein.com/2016/06/26/are-you-a-black-hole/#comments Sun, 26 Jun 2016 09:00:57 +0000 https://briankoberlein.com/?p=6060

You aren't a black hole, and that means a particle moving at nearly the speed of light isn't one either.

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One of the most popular questions asked about relativity concerns what would happen as an object approaches the speed of light. If it were moving fast enough, would it become a black hole? The same question could be asked another way: are you a black hole? The answer to the second question is obviously no. So is the answer to the first question. Confused? 

The basic argument is as an object approaches the speed of light from our perspective, three things happen. It’s time appears to slow down (time dilation), it appears to get shorter along its direction of travel (length contraction), and its mass appears to increase (relativistic mass).

These are all consequences of relativity and the fact that light has the same speed in all frames of reference. Relativity also says that a large enough mass in a small enough volume becomes a black hole. So it seems reasonable that an object near the speed of light should become a black hole.

If that were true, you must be a black hole.

Here’s why: the Universe is expanding. It’s not just that galaxies are racing away from us, space itself is expanding. This means that the more distant an object is from us, the faster it is moving away from us. There are distant galaxies moving away from us at nearly the speed of light. That means we are moving away from them at nearly light speed, so we should appear to be a black hole to them.

But the thing about black holes is that you either are one or aren’t one. A black hole’s event horizon must exist in all frames of reference. So if you aren’t a black hole in your frame of reference (and you’re not) then you’re not a black hole in any frame of reference. So a fast moving object does not become a black hole.

So what gives? It turns out the original argument is flawed. It’s true that an object’s relativistic mass does increase with speed. This means they are increasingly difficult to push, making it impossible for them to reach the speed of light. But everything is relative. From our perspective we have to keep pushing harder. From the object’s perspective our pushes keep getting smaller. As far as the object is concerned it’s mass hasn’t changed. So naturally it doesn’t become a black hole.

Just as you aren’t a black hole because you’re speeding away from distant galaxies. An object speeding away from us doesn’t become a black hole.

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