Black hole inside of a black hole... can it be done?

Gold Member
Let's say you have an absolutely giant black hole, so big that items inside of it leisurely approach the singularity, reaching it in about a million years (or whatever time it takes for a black hole to form from matter accumulation). Could matter slowly accumulating somehow form its own black hole on the way to the singularity? Why or why not?

Thanks!

(I won't speculate about machines that humans can use to create small black holes, because until we can do them, I feel that's going too far into science fiction. So no need to worry about a human going into a black hole and then making one on the way down.

Also, if I have the right formula, for proper time to be a million years, then the mass of the black hole would need to be ##M = \frac{1x10^6 y*c^3}{πG} =## 4.06 x 10^48 kg, which I think might be bigger than any black hole we've ever seen by a few orders of magnitude. So it certainly looks doubtful...
)

Algr and russ_watters

PeterDonis
Mentor
Could matter slowly accumulating somehow form its own black hole on the way to the singularity?
No. The definition of a black hole is a region of spacetime that cannot send light signals to infinity. Once you are inside such a region, you're inside it. The idea of having a second such region inside the first doesn't even make sense.

Dale
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2021 Award
Maybe a better question then is can you form a second singularity (through collapse) inside the horizon of a first singularity. I don’t see any reason why not.

russ_watters and Grasshopper
PeterDonis
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Maybe a better question then is can you form a second singularity (through collapse) inside the horizon of a first singularity.
No, you can't. The singularity is spacelike; once one is there, it already occupies the future of every event inside the horizon.

To put this another way: the "collapse" that ends in the singularity involves all matter that will ever cross the hole's horizon, not just the "original" collapsing object. All infalling worldlines end on the one singularity.

bhobba, SolarisOne, Grasshopper and 3 others
PeterDonis
Mentor
Maybe a better question
There is a question about multiple "things" inside a black hole horizon that could potentially have the answer "yes", but it's not either of the ones already asked in this thread. I believe it is possible to have multiple "trapped surfaces" (i.e., surfaces at which, locally, radially outgoing light does not move outward) inside a single horizon (and whose futures end in the same singularity). However, even this, AFAIK, requires very precisely tuned initial conditions.

bhobba, geshel, Grasshopper and 1 other person
Staff Emeritus
2021 Award
I agree there is no such thing as a BH inside a BH. I would even ask "how could you tell?"

I am a little curious about the following scenario. You have an observer in orbit far from a BH. Much farther out there is a thin spherical shell of dust moving radially inward, the mass is sufficiently large that when it forms a horizon the horizon radius is larger than that of the observer. Much much farther out there is a second observer. What do the observers see?

I think the outer observer case is simpler. He sees the dust rush in, and when it reaches the Schwarzchild radius, a horizon forms and he has a big BH where there was once a smaller one.

I am not sure what happens to the inner observer. I believe there is a time - before the large horizon forms - where he is unable to escape to infinity. I do not know if the inner observer sees the dust rush past him or not.

vanhees71
No, you can't. The singularity is spacelike; once one is there, it already occupies the future of every event inside the horizon.
When two blackholes collide to one, in some time in a merging process are there two singular points within a merged blackhole?

PS
In time reverse one black hole spit into two blackholes. It seems prohibited so such a BH merging should be an irreversible process.

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vanhees71
PeterDonis
Mentor
I think the outer observer case is simpler. He sees the dust rush in, and when it reaches the Schwarzchild radius, a horizon forms and he has a big BH where there was once a smaller one.
Yes.

I am not sure what happens to the inner observer. I believe there is a time - before the large horizon forms - where he is unable to escape to infinity.
This is correct except that "before the large horizon forms" needs to be changed to "before the large horizon reaches its larger radius". The event on the inner observer's worldline at which he can no longer escape to infinity (or send light signals there) is on the horizon, by definition; that event is where the horizon, as it moves outward from the original smaller radius to the new larger one, passes him.

I do not know if the inner observer sees the dust rush past him or not.
If the inner observer is in free fall, I think he will end up hitting the singularity before the dust passes him (but I have not tried to do the math to check this). However, if the inner observer is close enough to the original hole's horizon for this scenario to be workable, I'm not sure he can be in free fall, since there are no stable free-fall orbits inside ##r = 6M## and no free-fall orbits at all, even unstable ones, inside ##r = 3M##. If the inner observer is not in free fall, it's perfectly possible for him to accelerate in a way that allows him to see the dust fall past him before he hits the singularity.

martinbn
No, you can't. The singularity is spacelike; once one is there, it already occupies the future of every event inside the horizon.

To put this another way: the "collapse" that ends in the singularity involves all matter that will ever cross the hole's horizon, not just the "original" collapsing object. All infalling worldlines end on the one singularity.
Is this generically true or is this specific to say spherical collapse?

PeterDonis
Mentor
Is this generically true or is this specific to say spherical collapse?
For Reissner-Nordstrom or Kerr spacetime, if you take the maximal analytic extension, it is true that the singularity is timelike, not spacelike, and not all infalling worldlines will end on the singularity. However, in those maximally extended spacetimes, everything from the inner horizon inward (which includes the singularity) is beyond the Cauchy horizon of the exterior--i.e., it is impossible to predict what will actually be inside there from initial conditions specified in the exterior, unless you specify exact vacuum (or electrovacuum) everywhere (so that the maximal analytic extension is the solution)--which eliminates any such black hole that forms from the collapse of an actual material object. So those maximal analytic extensions don't seem trustworthy as a guide to what the interior of an actual charged or spinning black hole formed from the collapse of a charged or spinning object would be like. The only maximal analytic extension that does not have this problem is the Schwarzschild one--there is no Cauchy horizon in that case, so the interior of the maximal extension at least might be trustworthy as a rough guide to generic behavior.

To put this another way, we do not have any exact solutions for the collapse of a charged or spinning body to a Reissner-Nordstrom or Kerr black hole. The only exact solution we have for gravitational collapse of a material body is the Oppenheimer-Snyder model of spherically symmetric collapse to a Schwarzschild hole. We do, however, have numerical simulations of charged and spinning collapses, and as I understand it, they do one of two things: either the simulation blows up as the inner horizon is approached (because of the "infinite blueshift" problem at the inner horizon), or the simulation results in a singularity that is spacelike--i.e., it behaves the way the Schwarzschild black hole's singularity does. So, again, the Schwarzschild interior appears to be the one that is the best rough guide to what generic behavior should be expected in black hole interiors.

Aanta and martinbn
Gold Member
This is excellent stuff. But since @mitochan brought up colliding BHs, I have a related follow up question:

Nothing can travel faster than c, so would this not prevent two colliding BHs from ever instantly becoming one? Because presumably the two singularities are separated by a non-zero distance when the two event horizons meet.

On the other hand, at that point, clearly there is one singular future event for all matter in this composite BH. So would it be more practical to think of a singularity as a time rather than a location in space? (And in that case, would that not sidestep the issues of instantaneous information travel and of the distance separation between the two previous singularities, since by definition, all the matter will eventually reach one, singular fate?)

PeterDonis
Mentor
Nothing can travel faster than c, so would this not prevent two colliding BHs from ever instantly becoming one?
No.

the two singularities
There aren't two singularities. There is only one. The horizon of a black hole merger spacetime, heuristically, is shaped like a pair of trousers instead of a cylinder. The "legs" of the trousers are the two holes before the merger, and the upper part of the trousers is the single hole after the merger. The singularity is at the top of the trousers, to the future of everything inside the horizon.

Aanta and SolarisOne
PeterDonis
Mentor
would it be more practical to think of a singularity as a time rather than a location in space?
Not just more practical--correct, as opposed to wrong.

Grasshopper
timmdeeg
Gold Member
There aren't two singularities. There is only one.
The questions regarding a BH merger posed by @mitochan and @Grasshopper are assuming singularities. But what if physics "breaks down" at ##r=0## as most physicists are thinking? What if the mass exists in finite density in the center in a yet unknown state?
Could we still say there aren't two centers?

Dale
There aren't two singularities. There is only one. The horizon of a black hole merger spacetime, heuristically, is shaped like a pair of trousers instead of a cylinder. The "legs" of the trousers are the two holes before the merger, and the upper part of the trousers is the single hole after the merger. The singularity is at the top of the trousers, to the future of everything inside the horizon.
I draw a sketch for better understanding at attached.

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PeterDonis
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But what if physics "breaks down" at ##r=0## as most physicists are thinking? What if the mass exists in finite density in the center in a yet unknown state?
Could we still say there aren't two centers?
No. The "breakdown" area (roughly, where the spacetime curvature reaches the Planck scale) is still just one area, not two. And the spacetime location of that one area is just where I described, at the top of the trousers.

bhobba and timmdeeg
PeterDonis
Mentor
I draw a sketch for better understanding at attached.
Your sketch is incorrect. The topology of the singularity is a single spacelike line, not one line that branches into two.

mitochan
The topology of the singularity is a single spacelike line, not one line that branches into two.
The primitive deduction,

A BH as well as an ordinary body has a timelike line in our spacetime.
The center of BH has its timelike line also.
The singularity of BH lies in its center.
Thus singularity of BH is on a timelike line

would have one or more errors that I cannot point them out clearly.

PeterDonis
Mentor
A BH as well as an ordinary body has a timelike line in our spacetime.
The center of BH has its timelike line also.
The singularity of BH lies in its center.
Thus singularity of BH is on a timelike line
All four of these statements are false.

bhobba and PAllen
timmdeeg
Gold Member
No. The "breakdown" area (roughly, where the spacetime curvature reaches the Planck scale) is still just one area, not two. And the spacetime location of that one area is just where I described, at the top of the trousers.
Ok thanks. Does this mean that this area on Planck scale has not a location in space like the singularity and thus is not part of the manifold? If so then it would be misleading to say it is in the center of the black hole.

You said here
The mass of the eternal black hole is a global property of the spacetime geometry; there is no stress-energy associated with it." we have to distinguish two categories of black holes, the "real" one's which exist in our universe and which have stress-energy and the eternal black holes which haven't.
So it seems that the "global property of the spacetime geometry" of a black hole is represented by the mass regardless whether or not it is associated with stress-energy. On the other side how can something which has no location in space (in case the answer to the question above is yes) have stress-energy?

PeterDonis
Mentor
Does this mean that this area on Planck scale has not a location in space like the singularity and thus is not part of the manifold?
It means we don't know what the correct physics is in that area. The very concept of "part of the manifold" vs. "not part of the manifold" might not make sense.

If so then it would be misleading to say it is in the center of the black hole.
It's already misleading even in the purely classical GR model to say that the singularity is at the center of the black hole, and not because the singularity is strictly speaking not part of the manifold. There are still well-defined limits as ##r \to 0## that define "where the singularity is" in the spacetime. The key thing is that the singularity is a moment in time, not a place in space; it's spacelike, not timelike. A moment in time can't be "at the center" of anything.

how can something which has no location in space (in case the answer to the question above is yes) have stress-energy?
The singularity doesn't have stress-energy, nor does the region within a Planck scale of it. In spacetimes containing black holes formed by the collapse of a massive object, the stress-energy is in the region of spacetime occupied by the massive object.

bhobba, SolarisOne, Vanadium 50 and 1 other person
timmdeeg
Gold Member
The singularity doesn't have stress-energy, nor does the region within a Planck scale of it. In spacetimes containing black holes formed by the collapse of a massive object, the stress-energy is in the region of spacetime occupied by the massive object.
Thank you for clarifying this question.

timmdeeg
Gold Member
108 The concept of black hole 3: The global view shows diagrams of the head-on merger of two black holes.

Figure 4.18: Spacetime diagram of the event horizon corresponding to the head-on merger of two black holes as computed by Matzner et al. (1995)

Figure 4.19: Spacetime diagram showing the event horizon in the head-on merger of two black holes, as computed by Cohen et al. (2009)

Figure 4.21: Cross-section of the event horizon H of the spiraling merger of two black holes as computed by Cohen et al. (2012)

The first two diagrams show the trousers picture as mentioned by @PeterDonis in this Thread.

I have been searching for Eddington-Finkelstein diagrams which would eventually show the singularities - but not successful. A black hole in these coordinates is depicted in Figure 6.3 (page 136): Radial null geodesics of Schwarzschild spacetime, plotted in terms of ingoing EddingtonFinkelstein coordinates (t, r ˜ ).

Are there possibly principal reasons that one can't calculate the merger in Eddington-Finkelstein coordinates? Nevertheless the upper part of the legs (between them) of the trousers (Fig. 18 - 19) seems to mark the emergence of the new horizon.

Would it be correct that to assume the singularities in Fig. 4.19 within the trouser legs parallel to the horizon? This seems however to lead to the probably misleading notion that the two horizons are "unified" to one instantaneously at that upper part I mentioned above.

EDIT I just reread #12 where @PeterDonis said
There aren't two singularities. There is only one.
Does this mean if there are two Black holes which will collide in future then both have the "same" singularity. Then most I said above would be meaningless.

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PeterDonis
Mentor
Would it be correct that to assume the singularities in Fig. 4.19 within the trouser legs parallel to the horizon?
No. See my previous posts.

Does this mean if there are two Black holes which will collide in future then both have the "same" singularity.
Yes, at the top of the "trousers". See my previous posts.

timmdeeg
Staff Emeritus
2021 Award
However, if the inner observer is close enough to the original hole's horizon for this scenario to be workable, I'm not sure he can be in free fall

My original thought was that at time 1t you had the small black hole and at t2 you had the large black hole and that was that. Once the dust crosses a certain radius you go immediately from the old horizon to the new horizon. I no longer think that.

Here's why. The observer is orbiting at r, r1 < r < 2, where r1 is the initial Schwarzchild radius and r2 is the final one. To escape, he needs to travel from r to r2 before the outer horizon has formed. If he waits too long, he has to travel faster than c to do it, and that means he is now inside the horizon. So it can be said that the horizon (not a physical thing anyway) moves outward.

I was bugged by the shell theorem for a while. How can a spherical shell cause what is effectively an inward force? But the conditions do not apply when spacetime is this curved.