# Black hole inside a larger black hole.

by Meatbot
Tags: black, hole, inside
 PF Patron P: 247 Dear kev, I supposed you were talking about the interior of a black hole, and modeling it with a Schwarzschild vacuum. Indeed, a Schwarzschild interior solution models a static spherically symmetric fluid body, like a star, but I don't see how the interior of such black hole could be modeled with it, so I understood it in the first way. A swarm of stars existing inside its own Schwarzschild radius is a black hole, and the spacetime inside a black hole is clearly not static (one could better use a FRW solution for such spacetime), not because of moving masses, but because the "radius" of such spacetime as seen by external observers becomes timelike inside the black hole, so that your argument of checking the time dilation at a given radius seems quite incorrect. However, my point is simply to say, that to say that a "black hole inside a black hole" cannot have an event horizon you just need to look at the definition of an event horizon, no other demonstration is needed. However, this still does not prevent the existence of other kinds of absolute horizons inside a black hole (which may be practically considered black holes too, up to the exact definition of their horizon, also possibly, the horizons of all physical black holes may not be event horizons, as Hawking's definition is VERY constraining).
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 Quote by xantox ... (one could better use a FRW solution for such spacetime),,
In my last post I said "In fact that possibly makes the FRW metric a better method to analyse the swarm of stars." so we have some sort of agreement there although we differ on the reasons.

 Quote by xantox ...not because of moving masses, but because the "radius" of such spacetime becomes timelike, so that your argument of checking the time dilation at a given radius seems quite incorrect...
Yes, Kruskal-Szekeres coordinates and other interpretations suggest that spacelike intervals (our casual intuitive idea of distance) become timelike intervals (our casual intuitive idea of time).

It makes me wonder what would happen, if for example we had a distribution of galaxies and clusters within a ten billion light year radius (similar sort of scale to our visible universe) and the total mass of the galaxies was greater than the Schwarzschild density. Would we have no notion of what we normally think of as distance in that sort of a universe?

(You can think of this as a really BIG swarm of stars.)

Would such a hypothetical universe prevent the formation of conventional black holes within it? ..hmmmm... scratches chin...
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 Quote by kev Assuming that it is possible to concieve of a swarm of stars existing (temporarily) within its own Schwarzschild radius, then the interior Schwarzschild solution would suggest that any black hole at the centre would lose its event horizon.
kev. Perhaps you could back up and explain what you mean by a black hole at the centre.
Are you refering to the singularity of the large blackhole, or an additional blackhole that fell in?
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 Quote by Phrak kev. Perhaps you could back up and explain what you mean by a black hole at the centre. Are you refering to the singularity of the large blackhole, or an additional blackhole that fell in?
I meant an additional independent fully formed blackhole that was instantaneously inserted at the centre of the swarm of stars that initially had no mass located exactly at the centre.

Or perhaps better expressed as a small volume of radius r enclosing a mass of r*c^2/(2G) located at the centre of the swarm of stars where the total mass of the stars plus the enclosed black hole is R*c^2/(2G), where R is the radius of the swarm.

An alternative way of looking at it would be to consider a swarm of stars that has a density that marginally less than Schwarszchild density and is about to become a black hole. When the radius of the swarm is 9/8 R_s where R_s is the Schwarzschild radius, an event horizon forms at the centre. By event horizon I mean a region where the coordinate time dilation factor is zero. If you do like the idea of an event horizon that is not located at the Schwarzchild radius of the system then you can think of it as the dynamic zero coordinate time boundary. As the swarm continues to collapse, the zero time boundary (event horizon) moves outwards from the centre until it coincides with the Schwarschild radius of the swarm, at the exact moment the outermost stars arrive at the Schwarzschild radius. The conventional interpretation is that all the stars then continue to fall to eventually form a region that contains all the mass of the stars within a volume with zero radius at the centre, with infinite density (a singularity).
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I'm just trying to understand the physics of your analysing. I'm not well verse in this.

I pick up from Sean Carroll that the Schwartzchild metric applies to the vacuum about a spherically symmetric mass distribution--so it would even apply to the Earth. For a spherical surface within the vacuum that's between the event horizon and the swarm of star, a Kruskal diagram indicates that all future light rays are directed inward, just as for the event horizon. Even some space-like paths close to the light cone are directed inward.

So the first thing I notice is that it doesn't seem to make any sense to talk about a second event horizon (H2) within this vacuum region that's located between the event horizon (H1) and the swarm, right?

I take it that you propose that as the radial coordinate decreases deeper into the swarm of stars, the tilt of the light cone would become less, or at least allow that some future-directed rays would not terminate at r=0. The mass density of the swarm would become subcritical. (In analogy with Newtonian gravity, where the gravitational field due to a surrounding shell of matter is zero.) It would allow for the appearance of a second event horizon within the interior. Is this about right?
PF Patron
P: 247
 Quote by kev It makes me wonder what would happen, if for example we had a distribution of galaxies and clusters within a ten billion light year radius (similar sort of scale to our visible universe) and the total mass of the galaxies was greater than the Schwarzschild density. Would we have no notion of what we normally think of as distance in that sort of a universe?
An observer inside such sort of universe, provided it is big enough as you suggest, should see things looking quite normally, and would be able to measure usual distances and times, and the law of physics would be the same out there. However there has been an exchange of the external spatial radial and temporal coordinates. Since the metric coefficients become time-dependent, the internal spacetime is no longer static, but there are still 3 dimensions of space and 1 dimension of time. If you cut a section of fixed timelike "radius", it will look like a spacelike surface whose topology is now R^1xS^2 (Kantowski-Sachs spacetime). Very roughly, an infinite tube of time of finite spatial radius has been traded for a closed but unbounded universe of finite lifetime (so that a black hole interior has absolutely nothing to do with the structure of any common bodies such as stars).
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 Quote by xantox ...(so that a black hole interior has absolutely nothing to do with the structure of any common bodies such as stars).
umm. Yeah, but this is like talking special relativity without specifying an inertial frame.

I could just as validly say that the exterior of a black hole has absolutely nothing to do with the structure of common bodies such as stars.
 P: 241 Regarding the swarm of stars within it's own Schwarzschild radius, with a black hole inside of it, the first thing which came to my mind was a rotating maximal Kerr Metric.
 PF Patron P: 247 A maximal Kerr metric does not describe "a black hole containing a black hole", it describes a single rotating black hole with a limiting angular momentum, that is, a quite different beast.
 Sci Advisor P: 1,637 The problem with having a black hole inside a blackhole is several fold. Xantox is right, there is a problem with the horizon definition. Worse, there is a problem with the asymptotics. The asymptotics of the interior blackhole/star solution does not have minkowski space as a limit, so the very metric itself is poorly joined. In fact, it has some god awful time varying thing as an asymptote. The problem has indeed been looked at before, and its apparently one of the most excruciatingly complex things to do numerically in all of physics. The last time I talked with someone about it (I believe the state of the art is in Germany), they're still in rarefied extremal D != 4 situations with a bunch of highly technical assumptions which would take a specialist to explain, and even then, the computer returns junk most of the time.
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 Quote by Haelfix Worse, there is a problem with the asymptotics. The asymptotics of the interior blackhole/star solution does not have minkowski space as a limit, so the very metric itself is poorly joined. In fact, it has some god awful time varying thing as an asymptote.
I think you may have hit the nail on the head, Haelfix. Are you saying that, for an internal obsever, he doesn't have a finite region about him that is locally Minkowskian? That is, some place to keep a small interior blackhole??

If that's what your claiming, thats is a bit wierd, considering other statements made, that an infalling observer of a large black hole feels no perceptable change. I would take this to mean that the region around him continues to seem Minkowskian.
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 Quote by Chronos Concepts of time and space cease to be meaningful inside the event horizon of a black hole.
Unless someone is inside a BH??
Mentor
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 Quote by hurk4 Unless someone is inside a BH??
Look at the reply, post #6, by xantox.
 P: 2 Doesn't the universe satisfy the conditions of Almanzo's postulated star cluster inside its own schwarzchild radius? If so then every black hole is within the event horizon of a larger black hole. cf http://www.mathpages.com/home/kmath339.htm
 P: 6 The orbital velocity at the event horizon is the speed of light. Your black hole cannot orbit inside the event horizon of the other black hole because it cannot go faster than the speed of light. It instead falls in and does not orbit.
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 Quote by Haelfix The problem with having a black hole inside a blackhole is several fold. Xantox is right, there is a problem with the horizon definition. Worse, there is a problem with the asymptotics. The asymptotics of the interior blackhole/star solution does not have minkowski space as a limit, so the very metric itself is poorly joined. In fact, it has some god awful time varying thing as an asymptote. The problem has indeed been looked at before, and its apparently one of the most excruciatingly complex things to do numerically in all of physics. The last time I talked with someone about it (I believe the state of the art is in Germany), they're still in rarefied extremal D != 4 situations with a bunch of highly technical assumptions which would take a specialist to explain, and even then, the computer returns junk most of the time.
Any references to their work?