# Pair of supermassive black holes discovered on a collision course

July 10, 2019 8:21 PM Subscribe

A galaxy roughly 2.5 billion light-years away has a pair of supermassive black holes The titanic duo can help astronomers predict when the historic first detection of the background 'hum' of gravitational waves from supermassive black holes will be made and whether there truly is a 'final parsec problem'

I'm not 100% certain if they lose mass from colliding, because they also have available energy from the motion of orbiting each other, and I'm not an expert, but: If the point of the question is whether there are ways for black holes to lose mass, the answer is that black holes are predicted to lose mass through quantum pair production on either side of the horizon, called Hawking Radiation. They should eventually evaporate completely over trillions of trillions of years, starting when the universe becomes colder than the black hole (black holes have temperature inverse to their mass).

If the motivation is black holes losing mass seems to contradict the idea that "nothing can escape a black hole" this is because popular explanations of black holes are junk; black holes are

posted by I-Write-Essays at 9:37 PM on July 10, 2019 [7 favorites]

If the motivation is black holes losing mass seems to contradict the idea that "nothing can escape a black hole" this is because popular explanations of black holes are junk; black holes are

*much*weirder than that!posted by I-Write-Essays at 9:37 PM on July 10, 2019 [7 favorites]

APOD says the merger event GW150914 saw 31 and 36 solar mass black holes merge into a black hole of 63 solar masses.

So in that event, 4 solar masses were converted into gravitational waves.

(The page says 3, but their numbers don't add up — unless I'm getting this wrong somehow).

posted by jamjam at 10:07 PM on July 10, 2019 [1 favorite]

So in that event, 4 solar masses were converted into gravitational waves.

(The page says 3, but their numbers don't add up — unless I'm getting this wrong somehow).

posted by jamjam at 10:07 PM on July 10, 2019 [1 favorite]

*black holes are much weirder than that*

Yeah, I'm getting that.

posted by Joe in Australia at 10:17 PM on July 10, 2019 [1 favorite]

*popular explanations of black holes are junk*

Indeed. Black holes are not even holes. They're just the raggedy eroded edges of Now that don't have anything left underneath to stop stuff falling straight off into Later.

posted by flabdablet at 10:46 PM on July 10, 2019 [24 favorites]

I wish astronomers wouldn’t through around terms like “supermassive;” black holes have feelings, too.

Do you want to make them mad?

posted by GenjiandProust at 3:33 AM on July 11, 2019 [2 favorites]

Do you want to make them mad?

posted by GenjiandProust at 3:33 AM on July 11, 2019 [2 favorites]

Yes, the mass of the merged black hole is less than the sum of the mass of the two pre-merged black holes (as measured when the two black holes are "infinitely" far away from each other). You can think of this as the excess stress-energy (the generalization of mass/energy which is the thing that gravity really cares about) being radiated away in gravitational waves during the inspiral of the two black holes. So that merger of black holes really radiated away 4 solar masses worth of stress-energy. That's an amazing amount: a supernova emits only about a thousandth of a solar mass in electromagnetic energy, and a tenth of a solar mass in neutrinos.

This doesn't violate any properties of the "impermeability" of event horizons. Gravitational radiation of this sort is purely classical (in the sense that it doesn't involve any quantum behavior). Radiation is just the emission of waves in some medium; in this case the medium is "spacetime." Let's think about what a wave is: a wave is when you move one part of a medium away from some rest state, and due to the interconnectedness of the medium, that perturbation is forced to propagate away from that initial location. So for a wave on a guitar string, you pull the string away in one spot, and when you release it, the dynamics of the string not only force that spot to oscillate around its equilibrium, but also that the locations next to that spot also must start moving, and the locations next to those locations, and so on and so forth. Ta da: a wave.

When you move a source of stress-energy around in spacetime, the Einstein equations of GR imply that spacetime near the mass is forced to change, reacting to the presence of the stress-energy. But in order for spacetime to remain continuous and smooth, the spacetime further away from that mass is also forced to react as well, and so on and so forth. If you move stress-energy around in the right way, that cascade of reactions in spacetime will look like what we call a "wave." (Obviously, the waving here is much more complicated than a guitar string because, you know, the thing that's waving is also the thing that's telling you about "where" and "when," but the math is more or less the same.)

I present it this way to explain why there's nothing disturbing about black holes with event horizons from creating waves: the wave isn't coming from "inside" the event horizons. The waves are due to the spacetime *next* to the event horizon changing to maintain continuity as the two event horizon themselves spin around each other (and indeed, we don't need black holes for measurable gravitational waves. Compact objects like neutron stars will serve just as well, and they don't have event horizons).

This is why we can predict gravitational waves using non-quantum GR: we don't need to understand anything "inside" the black hole to get the result. Now, we could hope that in very extreme situations (like, two black holes merging) we might see quantum effects in gravitational waves, as any classical process is just a particular limit of quantum effects, and we do expect that our classical understanding of gravity to have additional quantum terms that we don't know about yet. However, as I understand it, so far the details of all gravitational radiation we have seen is consistent with our classical understanding of general relativity. Which is of course frustrating, as while we physicists like being right, but also would prefer that when we're right we also find things we don't understand.

Also, the Universe doesn't need to conserve the mass of black holes (hell, the Universe doesn't even really care about conserving energy). The thing that the Universe really cares about is whether entropy increases (ok, it also wants to conserve stress-energy in some sense). Black hole event horizons carry entropy proportional to the their surface area, so the only important thing is whether the final black hole has greater surface area than the sum of the two pre-merged black holes. I will assert (without looking up the spin of all the black holes involved in the event), that in GW150914, this inequality is satisfied, because the only law of physics I'm not ok violating is the 2nd Law of Thermodynamics (the spin matters because the event horizon of a black hole depends on the mass and the angular momentum, see my comments on the Event Horizon Telescope image).

Hawking radiation decreases the surface area of a black hole, but does so by creating a thermal bath of particles outside of the black hole, increasing the total entropy of the Universe in the process. Entropy and gravity have some deep connection which we don't fully understand. Which is why the real use-case for faster-than-light travel is not cruising around the Universe or even going back in time, but localized reduction of entropy (and if you think about it, isn't time travel just reducing entropy?). This is also why, if you get your choice of superpowers, pick "ability to reduce entropy at will" and hope that the superpower-granting entity doesn't understand that it just made you all-powerful.

posted by physicsmatt at 6:23 AM on July 11, 2019 [35 favorites]

This doesn't violate any properties of the "impermeability" of event horizons. Gravitational radiation of this sort is purely classical (in the sense that it doesn't involve any quantum behavior). Radiation is just the emission of waves in some medium; in this case the medium is "spacetime." Let's think about what a wave is: a wave is when you move one part of a medium away from some rest state, and due to the interconnectedness of the medium, that perturbation is forced to propagate away from that initial location. So for a wave on a guitar string, you pull the string away in one spot, and when you release it, the dynamics of the string not only force that spot to oscillate around its equilibrium, but also that the locations next to that spot also must start moving, and the locations next to those locations, and so on and so forth. Ta da: a wave.

When you move a source of stress-energy around in spacetime, the Einstein equations of GR imply that spacetime near the mass is forced to change, reacting to the presence of the stress-energy. But in order for spacetime to remain continuous and smooth, the spacetime further away from that mass is also forced to react as well, and so on and so forth. If you move stress-energy around in the right way, that cascade of reactions in spacetime will look like what we call a "wave." (Obviously, the waving here is much more complicated than a guitar string because, you know, the thing that's waving is also the thing that's telling you about "where" and "when," but the math is more or less the same.)

I present it this way to explain why there's nothing disturbing about black holes with event horizons from creating waves: the wave isn't coming from "inside" the event horizons. The waves are due to the spacetime *next* to the event horizon changing to maintain continuity as the two event horizon themselves spin around each other (and indeed, we don't need black holes for measurable gravitational waves. Compact objects like neutron stars will serve just as well, and they don't have event horizons).

This is why we can predict gravitational waves using non-quantum GR: we don't need to understand anything "inside" the black hole to get the result. Now, we could hope that in very extreme situations (like, two black holes merging) we might see quantum effects in gravitational waves, as any classical process is just a particular limit of quantum effects, and we do expect that our classical understanding of gravity to have additional quantum terms that we don't know about yet. However, as I understand it, so far the details of all gravitational radiation we have seen is consistent with our classical understanding of general relativity. Which is of course frustrating, as while we physicists like being right, but also would prefer that when we're right we also find things we don't understand.

Also, the Universe doesn't need to conserve the mass of black holes (hell, the Universe doesn't even really care about conserving energy). The thing that the Universe really cares about is whether entropy increases (ok, it also wants to conserve stress-energy in some sense). Black hole event horizons carry entropy proportional to the their surface area, so the only important thing is whether the final black hole has greater surface area than the sum of the two pre-merged black holes. I will assert (without looking up the spin of all the black holes involved in the event), that in GW150914, this inequality is satisfied, because the only law of physics I'm not ok violating is the 2nd Law of Thermodynamics (the spin matters because the event horizon of a black hole depends on the mass and the angular momentum, see my comments on the Event Horizon Telescope image).

Hawking radiation decreases the surface area of a black hole, but does so by creating a thermal bath of particles outside of the black hole, increasing the total entropy of the Universe in the process. Entropy and gravity have some deep connection which we don't fully understand. Which is why the real use-case for faster-than-light travel is not cruising around the Universe or even going back in time, but localized reduction of entropy (and if you think about it, isn't time travel just reducing entropy?). This is also why, if you get your choice of superpowers, pick "ability to reduce entropy at will" and hope that the superpower-granting entity doesn't understand that it just made you all-powerful.

posted by physicsmatt at 6:23 AM on July 11, 2019 [35 favorites]

*Hawking radiation decreases the surface area of a black hole, but does so by creating a thermal bath of particles outside of the black hole, increasing the total entropy of the Universe in the process.*

And I presume gravitational waves do the same, increasing entropy by shaking things around as they pass? Otherwise that reduction in mass / surface area has to go somewhere, right?

posted by Joe in Australia at 7:25 AM on July 11, 2019

Nope: that's what I meant by gravitational waves being a classical GR phenomenon. The gravitational waves are non-thermal and essentially monochromatic (that is, the waves are all emitted at the same frequency at any moment in the inspiral), so they have zero entropy (ignoring the very final waves at the end of the chirp). I'm therefore asserting that the merger of two black holes will result in a black hole with larger surface area than the sum of the two original black holes (and thus larger entropy).

Having gone out on a limb saying that the merger resulted in a black hole with larger entropy than the initial two, I'm glad to see that this seems to be compatible with the data, at least given the current accuracy of our measurements. Assuming the two initial black holes had no intrinsic spin, the entropy of each is proportional to their surface areas:

A = 16\pi G M^2.

Where G is Newton's constant. Now, we have M_1 = 29 and M_2 = 36 solar masses, while the final mass is M_f = 62 M_sol. So, in this approximation, if 29^2+36^2 is less than 62^2, then the surface area increases and the 2nd Law is fine, and indeed

29^2+36^2 = 2137 < 3844 = 62^2,

so everything looks great, if you consider increasing entropy and thus the inevitable heat-death of the Universe to be a good thing.

However, this isn't the end of the story. Real black holes almost always have intrinsic spin, which has a maximum value for a given mass black hole. This is because spin causes the event horizon to move *in* towards the singularity while at the same time turning the point singularity into a ring (a ringularity) which increases in radius as the spin increases. Spin larger than maximal would result in the event horizon being inside the ringularity's radius, and we don't like naked singularities.

Now in the GW150914 merger, the two initial black holes are consistent with having zero spin (they probably don't have exactly zero spin, but the data isn't good enough to know for sure. Also, increasing their spin will only decrease the initial surface area, and thus make it easier for the inequality to be satisfied). The final black hole appears to have a spin of ~2/3rds maximal, with large error bars. The surface area of a Kerr (spinning) black hole is

A = 8\pi G M^2(1+sqrt(1-a^2))

where a is this spin parameter that can at most be 1. Plugging in the parameters for this merger, we get a surface area of

16\pi G * 3348 M_sol^2>16\pi G(29^2+36^2).

This still satisfies the inequality: entropy still increases. Indeed, the inequality is satisfied and entropy increases for final spins less than 99.37% of maximal.

You might be bothered that it looks like there is a way for the 2nd law to be violated here, if the final spin is large enough, then the black hole entropy decreases. But that final spin is in part set by how much energy is radiated away (and thus how big the final event horizon is). A merger that results in higher spin must therefore radiate less energy away in gravitational waves. But we didn't enforce that condition by hand: it just comes out of how gravity will pull these two masses together. So gravity will conspire to force entropy to increase

THAT is a very deep point about the Universe, and I have no idea what it means.

posted by physicsmatt at 7:59 AM on July 11, 2019 [21 favorites]

Having gone out on a limb saying that the merger resulted in a black hole with larger entropy than the initial two, I'm glad to see that this seems to be compatible with the data, at least given the current accuracy of our measurements. Assuming the two initial black holes had no intrinsic spin, the entropy of each is proportional to their surface areas:

A = 16\pi G M^2.

Where G is Newton's constant. Now, we have M_1 = 29 and M_2 = 36 solar masses, while the final mass is M_f = 62 M_sol. So, in this approximation, if 29^2+36^2 is less than 62^2, then the surface area increases and the 2nd Law is fine, and indeed

29^2+36^2 = 2137 < 3844 = 62^2,

so everything looks great, if you consider increasing entropy and thus the inevitable heat-death of the Universe to be a good thing.

However, this isn't the end of the story. Real black holes almost always have intrinsic spin, which has a maximum value for a given mass black hole. This is because spin causes the event horizon to move *in* towards the singularity while at the same time turning the point singularity into a ring (a ringularity) which increases in radius as the spin increases. Spin larger than maximal would result in the event horizon being inside the ringularity's radius, and we don't like naked singularities.

Now in the GW150914 merger, the two initial black holes are consistent with having zero spin (they probably don't have exactly zero spin, but the data isn't good enough to know for sure. Also, increasing their spin will only decrease the initial surface area, and thus make it easier for the inequality to be satisfied). The final black hole appears to have a spin of ~2/3rds maximal, with large error bars. The surface area of a Kerr (spinning) black hole is

A = 8\pi G M^2(1+sqrt(1-a^2))

where a is this spin parameter that can at most be 1. Plugging in the parameters for this merger, we get a surface area of

16\pi G * 3348 M_sol^2>16\pi G(29^2+36^2).

This still satisfies the inequality: entropy still increases. Indeed, the inequality is satisfied and entropy increases for final spins less than 99.37% of maximal.

You might be bothered that it looks like there is a way for the 2nd law to be violated here, if the final spin is large enough, then the black hole entropy decreases. But that final spin is in part set by how much energy is radiated away (and thus how big the final event horizon is). A merger that results in higher spin must therefore radiate less energy away in gravitational waves. But we didn't enforce that condition by hand: it just comes out of how gravity will pull these two masses together. So gravity will conspire to force entropy to increase

**even though you didn't ask it to.**THAT is a very deep point about the Universe, and I have no idea what it means.

posted by physicsmatt at 7:59 AM on July 11, 2019 [21 favorites]

thanks

I lack the knowledge/education to understand this pretty much at all, but your explanations make me feel a glimmer of insight. this is really fascinating!

posted by supermedusa at 8:54 AM on July 11, 2019

**physicsmatt**!I lack the knowledge/education to understand this pretty much at all, but your explanations make me feel a glimmer of insight. this is really fascinating!

posted by supermedusa at 8:54 AM on July 11, 2019

Yes, thank you for your contributions, physicsmatt. You are really good at explaining difficult, interesting stuff (assuming what I understood at least approximates what you were trying to say, which I probably shouldn't, but I am, if nothing else, fascinated).

posted by straight at 9:06 AM on July 11, 2019 [2 favorites]

posted by straight at 9:06 AM on July 11, 2019 [2 favorites]

Glad you enjoyed it. Working through the problem gave me another chance to think about some quirks of gravity and entropy, which is always a treat for me. Still no idea what it all means, unfortunately.

posted by physicsmatt at 10:52 AM on July 11, 2019 [1 favorite]

posted by physicsmatt at 10:52 AM on July 11, 2019 [1 favorite]

physicsmatt: "

This is something I find fascinating as a recovering ChemE. My knowledge of Thermo mostly comes from Chemical Thermo, usually from the Gibbs way of looking at things. So my knowledge of Stat thermo is rudimentary at best.

One of the things I remember is that the Second Law as was taught to me came from the Kinetic theory of gases (involved math, but understandable). But it is when I read about Thermodynamics on its own; that the Second Law got fully weird. The fact that it pops up all over the place deeply embedded, especially whenever energy is involved is something that I find utterly inexplicable.

I tried reading Ilya Prigogine but found it quite incomprehensible. Can you recommend any books/articles for me to get a better understanding of the Second Law and Thermo in general? I did read the "Thermodynamics: A Very Short Introduction" by Atkins in the Oxford series and found it quite good. I am looking for something like that, but a little more fleshed out. Thanks

posted by indianbadger1 at 12:59 PM on July 11, 2019

*So gravity will conspire to force entropy to increase even though you didn't ask it to."*This is something I find fascinating as a recovering ChemE. My knowledge of Thermo mostly comes from Chemical Thermo, usually from the Gibbs way of looking at things. So my knowledge of Stat thermo is rudimentary at best.

One of the things I remember is that the Second Law as was taught to me came from the Kinetic theory of gases (involved math, but understandable). But it is when I read about Thermodynamics on its own; that the Second Law got fully weird. The fact that it pops up all over the place deeply embedded, especially whenever energy is involved is something that I find utterly inexplicable.

I tried reading Ilya Prigogine but found it quite incomprehensible. Can you recommend any books/articles for me to get a better understanding of the Second Law and Thermo in general? I did read the "Thermodynamics: A Very Short Introduction" by Atkins in the Oxford series and found it quite good. I am looking for something like that, but a little more fleshed out. Thanks

posted by indianbadger1 at 12:59 PM on July 11, 2019

*Entropy and gravity have some deep connection which we don't fully understand.*

I appreciate your taking the time to share your expertise with us, as always. If you chose to expand on this bit I would pay rapt attention.

posted by PMdixon at 6:21 PM on July 11, 2019 [1 favorite]

*we don't like naked singularities*

Speak for yourself 8-/

posted by HiroProtagonist at 7:40 PM on July 11, 2019 [1 favorite]

*gravity will conspire to force entropy to increase even though you didn't ask it to.*

THAT is a very deep point about the Universe, and I have no idea what it means.

THAT is a very deep point about the Universe, and I have no idea what it means.

I prefer to take it as fundamental that entropy will always increase with time, regardless of any other consideration, on the basis that that's what time

*is*. I see gravity as a kind of self-organizing but ultimately futile resistance to the inevitability of that, a side effect of the traffic jam of mass.

posted by flabdablet at 9:49 PM on July 11, 2019

I'm curious - why do top physicists regard the second law of thermodynamics (Entropy always increases) as the most inviolable of all the laws in physics - I've seen this not just from physicsmatt above, but other eminent physicists like Sean Carroll, Kip Thorne and others have both made a similar assertion. As a law it is fairly easy to construct thought experiments that might break it (e.g. Maxwell's Demon) though none have been successful.

We have other beautiful theories (GR, QM) though with both of those, we know that something must break to make them agree with each other at the Planck scale. We know that the first law of thermodynamics can be broken at large scales (dark energy), and the third law of thermodynamics (Entropy at 0 kelvin = 0) is mostly a subset of the second law.

posted by BigCalm at 1:33 AM on July 12, 2019

We have other beautiful theories (GR, QM) though with both of those, we know that something must break to make them agree with each other at the Planck scale. We know that the first law of thermodynamics can be broken at large scales (dark energy), and the third law of thermodynamics (Entropy at 0 kelvin = 0) is mostly a subset of the second law.

posted by BigCalm at 1:33 AM on July 12, 2019

My father, a Physical Chemist who taught Biochemistry, also regarded the 2nd law as invioable. I think it's because most folks who think that way are not quantum physicists, and are convinced the arrow of time is also invioable, though a lot of evidence is stacking up against that, as I understand it. At least in the quantum physics worlds, or some of them.

You know, the scientific method asks us to completely divorce our senses and sensibilities from the actual doing of research, and the thinking about and writing about science. But IME, even the best researchers can only do this a little bit more than any other person in the world. We ask a lot of ourselves but our minds and bodies firmly root us in the here and now, and have us experience time as unrolling in only one direction (into the future).

It would be easier to be more objective if we didn't have bodies or senses, I suppose. But then how would we research the real world?

posted by kalessin at 4:43 AM on July 12, 2019

You know, the scientific method asks us to completely divorce our senses and sensibilities from the actual doing of research, and the thinking about and writing about science. But IME, even the best researchers can only do this a little bit more than any other person in the world. We ask a lot of ourselves but our minds and bodies firmly root us in the here and now, and have us experience time as unrolling in only one direction (into the future).

It would be easier to be more objective if we didn't have bodies or senses, I suppose. But then how would we research the real world?

posted by kalessin at 4:43 AM on July 12, 2019

I'd say when you really get the 2nd law it's basically a tautology. It's not reliant on any particular aspect of physics - it's more like a statement that you'll probably see something probable happen instead of something improbable. It's working on a level of quite pure considerations about physical systems that could apply to a range of laws of physics, not just the ones we happen to have formulated.

So if gravity turned out to work slightly differently or electromagnetism worked out slightly differently than we thought then that'd not be all that surprising. But when you're talking about entropy increasing it pretty much has to, almost from how it's defined. You might find that if you come up with some new bit of physics you have to account for entropy in a way you hadn't previously considered (like, as the area of the event horizon of black holes) but the 2nd law itself is going to work as you expect once you've done that.

Maybe it's better to think of it as a consequence of a basic framework into which a whole range of possible laws of physics could be put, than as being something on the same level as those other laws.

posted by edd at 6:45 AM on July 12, 2019 [3 favorites]

So if gravity turned out to work slightly differently or electromagnetism worked out slightly differently than we thought then that'd not be all that surprising. But when you're talking about entropy increasing it pretty much has to, almost from how it's defined. You might find that if you come up with some new bit of physics you have to account for entropy in a way you hadn't previously considered (like, as the area of the event horizon of black holes) but the 2nd law itself is going to work as you expect once you've done that.

Maybe it's better to think of it as a consequence of a basic framework into which a whole range of possible laws of physics could be put, than as being something on the same level as those other laws.

posted by edd at 6:45 AM on July 12, 2019 [3 favorites]

edd, the thing that makes me disagree with that statement is the fact that there are energy conjectures in general relativity which, if violated, could lead to entropy decreases in black holes. Violating these doesn't seem like a problem from a field theoretic viewpoint, but it seems the Universe has decided to respect them (also, violating these conditions is how you get time travel. Though the arrow of time is basically defined by entropy, so I guess this observation could be seen as a tautology).

posted by physicsmatt at 7:26 AM on July 12, 2019 [4 favorites]

posted by physicsmatt at 7:26 AM on July 12, 2019 [4 favorites]

I wonder, if you do allow a stress tensor that violates your favorite energy condition, does the state counting that matches black hole horizon areas to a micro state counting also get messed up? Are there any sufficiently supersymmetric systems where we could imagine having control over microstate counting but also violating, say, the null energy condition?

I guess philosophically I agree more with edd, especially because we only associated black hole areas with entropies because they play the correct thermodynamic role (among other things, they obey the generalized second law). It wasn’t until decades later before anyone had a proper microstate counting for any black holes (let alone for the non SUSY ones we see in the sky).

One way to resolve the two viewpoints (edd vs physicsmatt) is for the association between black hole entropy and area to fail exactly when an energy condition is violated that would allow for violation of the second law.

Another is if systems which allow for violation of eg null energy condition are themselves unphysical. Since most laws of physics are time reversal invariant (add a C or P if needed), then usually we can write down a solution to a system of equations that does the wrong thing— e.g. sends all the air molecules into a tiny corner of the room— but those are unphysical solutions, since any tiny, unavoidable variation in how you set the system up means the end state would again have the molecules spread out in the whole room. This is in much the same way as naked singularities can often only be formed by a fine-tuned set of initial conditions (thanks cosmic censorship).

I think probably this second resolution is correct, but it would be kind of fun if the first were instead.

posted by nat at 6:37 PM on July 12, 2019

I guess philosophically I agree more with edd, especially because we only associated black hole areas with entropies because they play the correct thermodynamic role (among other things, they obey the generalized second law). It wasn’t until decades later before anyone had a proper microstate counting for any black holes (let alone for the non SUSY ones we see in the sky).

One way to resolve the two viewpoints (edd vs physicsmatt) is for the association between black hole entropy and area to fail exactly when an energy condition is violated that would allow for violation of the second law.

Another is if systems which allow for violation of eg null energy condition are themselves unphysical. Since most laws of physics are time reversal invariant (add a C or P if needed), then usually we can write down a solution to a system of equations that does the wrong thing— e.g. sends all the air molecules into a tiny corner of the room— but those are unphysical solutions, since any tiny, unavoidable variation in how you set the system up means the end state would again have the molecules spread out in the whole room. This is in much the same way as naked singularities can often only be formed by a fine-tuned set of initial conditions (thanks cosmic censorship).

I think probably this second resolution is correct, but it would be kind of fun if the first were instead.

posted by nat at 6:37 PM on July 12, 2019

Oh also, actually about the article, is there an astrophysicist around who can explain the final parsec problem to me? As someone really used to the idea that two nearby black holes (with only empty space around them) should be described just by their mass and angular momenta (and relative angular momentum) — and since such a system emits gravitational waves it must lose energy — it seems like the only possible end state is a merger. So, how do the stars and other matter around the supermassive black holes mess this up? Is there somehow a (meta)stable system involving two black holes orbiting each other and a ton of stars orbiting both of them?

posted by nat at 6:47 PM on July 12, 2019

posted by nat at 6:47 PM on July 12, 2019

(I don't have any argument with physicsmatt of course, who certainly knows an awful lot more than I do. I think the commonplace phrasing of the second law as inviolable is probably not meant in reference to such unusual circumstances which most scientists who have to use thermodynamics in anger wouldn't know about, so I don't think there's any deep disagreement and only a source of lots of interesting things to find out about.)

On the final parsec problem I think it's just a matter of how different processes scale. For both stellar mass and supermassive hole pairs you'll need astrophysical processes to get the two close enough for gravitational radiation to take over, and it's just that stellar mass ones can get to that point more easily. Once either type are close enough gravitational radiation can take over.

Any two orbiting bodies will emit gravitational radiation but it scales so that the merger time for starting at a given distance r is proportional to r^4. So doubling the distance at the start increases the time to merge by a factor of 16. The end state for a supermassive pair at a parsec is still a merged hole but on a timescale way longer than the age of the universe so far. It's not that other matter has messed up the merger, it's that it hasn't been able to do enough to get the pair close enough by other means initially.

posted by edd at 2:43 AM on July 13, 2019

On the final parsec problem I think it's just a matter of how different processes scale. For both stellar mass and supermassive hole pairs you'll need astrophysical processes to get the two close enough for gravitational radiation to take over, and it's just that stellar mass ones can get to that point more easily. Once either type are close enough gravitational radiation can take over.

Any two orbiting bodies will emit gravitational radiation but it scales so that the merger time for starting at a given distance r is proportional to r^4. So doubling the distance at the start increases the time to merge by a factor of 16. The end state for a supermassive pair at a parsec is still a merged hole but on a timescale way longer than the age of the universe so far. It's not that other matter has messed up the merger, it's that it hasn't been able to do enough to get the pair close enough by other means initially.

posted by edd at 2:43 AM on July 13, 2019

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posted by Joe in Australia at 9:17 PM on July 10, 2019