Black hole inside a larger black hole.

[Meatbot]

Could a smaller black hole orbit the center of a larger black hole at a distance less than the larger hole's event horizon? What would happen? Seems like nothing unusual but it was an interesting idea.

 

[xantox]

No, it couldn't. As the black holes become close, their orbits will become highly nonlinear, their horizons will deform, strong gravitational waves will be emitted, and they will ultimately merge into a single black hole.

 

[Almanzo]

While black holes might not orbit inside other black holes, a situation might exist which would allow one to speak of a black hole existing inside another black hole.

Consider a swarm of stars, somewhat like a star cluster. If the stars are close enough to their neighbours, and the swarm is large enough, the swarm as a whole will exist inside its own Schwarzschild Radius. (This might not be a stable or long-lasting situation, but it can be conceived of.) The stars do not have to touch or even approach each other more closely than the Sun and the Earth to ensure this; the usual descriptions of ultra high densities, ultra strong gravity, ultra high speeds, etc. are therefore inessential to the concept of a black hole.

Now, one of the stars might be a black hole in its own right. This is possible because the radius of a black hole (the Schwarzschild Radius) is proportional to its mass, which makes the (apparent) density of the hole inversely proportional to the square of its mass. The star would (for the moment, at least) have a much higher density than the swarm of stars, and therefore it would be allowed to be smaller.

 

[xantox]

Now, one of the stars might be a black hole in its own right.

Yes, but you must carefully consider that the standard meaning of the term "black hole" in the underlining theory is based on the existence of a global event horizon, which is not applicable to such inner body. So, some different kind of surface should be identified to describe it, which is not a trivial task (this is an active field of research in numerical relativity).

 

[Chronos]

Concepts of time and space cease to be meaningful inside the event horizon of a black hole.

 

[xantox]

Concepts of time and space cease to be meaningful inside the event horizon of a black hole.

No, they remain perfectly meaningful, excepted near the singularity.

 

[Phrak]

Something doesn't seem right here...

From the perspective of a sufficiently distant observer the event horizons murge. But the question is about a black hole within the event horizon. This requires a different coordinate chart.

As I fall through the event horizon of a large fluffy black hole, I take my little black hole with me. I keep it in a shoe box. Nothing odd here--except that infinite time has transpired in the rest of the universe as I cross the event horizon.

Then again, how do find myself on the other side of the event horizon of a black hole that has evaporated in finite time?

The Usenet Physics FAQ assures me that the event horizon will be waiting and ready when I decide to crosss it. What gives?

 

[MeJennifer]

Consider a swarm of stars, somewhat like a star cluster. If the stars are close enough to their neighbours, and the swarm is large enough, the swarm as a whole will exist inside its own Schwarzschild Radius. (This might not be a stable or long-lasting situation, but it can be conceived of.)

Interesting proposition.

Any references to the literature?

 

[Margiani]

Future Binary system; small Black hole to a larger black hole.

Thermal radiation of the Sirius prevents cooling of the exploded star’s core. The remnant could not produce black hole and still visible as a white Ultra Dense Nucleus (a white dwarf of type DA2). It will produce micro-quasar to the carbon-Sirius, black hole - to the pulsar of Sirius and last stage will be binary system of black holes. Pulsar of the Sirius will not prevent gnome’s cooling evolution

 

[xantox]

Something doesn't seem right here...

From the perspective of a sufficiently distant observer the event horizons murge. But the question is about a black hole within the event horizon. This requires a different coordinate chart.

Nothing forbids the presence of an horizon inside a black hole, however it cannot be an event horizon by definition. But you could find another definition for it, such as a future outer trapping horizon.

 

[Phrak]

Nothing forbids the presence of an horizon inside a black hole, however it cannot be an event horizon by definition. But you could find another definition for it, such as a future outer trapping horizon.

I found this (or these) definitions for the event horizon on Wikipedia.

"The most commonly known example of an event horizon is defined around general relativity's description of a black hole, a celestial object so dense that no matter or radiation can escape its gravitational field. This is sometimes described as the boundary within which the black hole's escape velocity is greater than the speed of light. "

From the perspective of the guy falling into the larger black hole taking a smaller black hole with him there is no problem with the definition. The definition is inappropriate over all coordinate maps. That's not suprising really.

Where is the event horizon from the perspective inside the black hole?

 

[yuiop]

Consider a swarm of stars, somewhat like a star cluster. If the stars are close enough to their neighbours, and the swarm is large enough, the swarm as a whole will exist inside its own Schwarzschild Radius. (This might not be a stable or long-lasting situation, but it can be conceived of.)

Interesting proposition.

Any references to the literature?

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.

The gravitational time dilation factor at any radius within the swarm can be calculated from the interior solution (which is apropriate here) by taking densities into account and it can be shown the time dilation at the Schwarzschild radius of the interior black hole is no longer zero and the interior black hole will technically no longer be a black hole. This is because in gravitational time dilation in GR is affected by mass inside AND OUTSIDE the enclosed volume at any given radius. The Newtonian concept of outer shells of mass having no gravitational effect on interior shells is not valid in GR.

 

[xantox]

I found this (or these) definitions for the event horizon on Wikipedia

The actual formal definitions of an event horizon shall be taken from Hawking, or Wald. An event horizon is the future boundary of the causal past of future null infinity, in a weakly asymptotically flat spacetime.

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.

A Schwarzschild solution is about empty space, so it cannot apply to the interior of a non-empty black hole such as this swarm of stars.

 

[MeJennifer]

A Schwarzschild solution is about empty space, so it cannot apply to the interior of a non-empty black hole such as this swarm of stars.

Exactly.

I would be carefull in assuming that a bunch of spread out black holes would create some bigger common event horizon. I am not saying it is impossible but I never heared of any theorems that actually show that.

 

[yuiop]

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.

A Schwarzschild solution is about empty space, so it cannot apply to the interior of a non-empty black hole such as this swarm of stars.

Exactly.
...

I was careful to specify the interior Schwarzschild solution which covers that part of a spherical non rotating gravitational field that is not empty space.

For example the spacetime within the Earth's atmosphere and below the surface of the Earth itself would be described by the interior Schwarzschild solution if you ignore rotation and inhomogenuities like the moon, Sun and galaxies in the exterior part.

A swarm of stars would be loosely described by the interior Schwarzschild solution if you make the aproximation that the mass is distributed evenly rather than concentrated in the stars. The FRW metric for the universe as a whole makes a similar sort of aproximation that the mass of galaxies is evenly spread out in space and ignores the fact that most of the mass is actually highly concentrated in localised regions.

 

[MeJennifer]

A swarm of stars would be loosely described by the interior Schwarzschild solution if you make the aproximation that the mass is distributed evenly rather than concentrated in the stars. The FRW metric for the universe as a whole makes a similar sort of aproximation that the mass of galaxies is evenly spread out in space and ignores the fact that most of the mass is actually highly concentrated in localised regions.

The Schwarzschild and FRW solutions give completely different effects.

A swarm of stars would be loosely described by the interior Schwarzschild solution if you make the aproximation that the mass is distributed evenly rather than concentrated in the stars.

Is that a conclusion that is drawn from GR or just your guess?

 

[xantox]

I was careful to specify the interior Schwarzschild solution which covers that part of a spherical non rotating gravitational field that is not empty space.

Even if you take a perfect fluid solution, you're still considering an idealized metric which is assumed not to contain any black hole-like object in the first place. So how can you deduce from that anything about the (im-)possibility of black hole-like objects inside this space?

 

[yuiop]

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.

A Schwarzschild solution is about empty space, so it cannot apply to the interior of a non-empty black hole such as this swarm of stars.

Even if you take a perfect fluid solution, you're still considering an idealized metric which is assumed not to contain any black hole-like object in the first place. So how can you deduce from that anything about the (im-)possibility of black hole-like objects inside this space?

You have not been honest enough to admit, that your counter statement in response to my statement about the interior Schwarzschild solution, that the Schwarzschild solution is about empty space, is simpy wrong and misleading in this context.

In your later statement you mention the "fluid solution" which I take as as indirect acknowledgment that you agree that there is a Schwarzschild solution that is not about empty space?

I do agree that I am considering an idealized metric, because in a complex situation some simplifying assumptions is a good place to start the analysis and is better than "nothing", where nothing about sums up your contribution to how the swarm of stars would be analysed.

To use the interior Schwarzschild solution, then yes, you do have to assume you know something about how the mass in the total volume is distributed. I have also made the assumption that variations in density can be handled but to keep the math relatively straight forward then a simplified model made up of concentric shells of varying density is a also a good place to start. That is one reason that I specified that the black hole enclosed with the swarm of stars is at the centre of the swarm. An enclosed black hole that was off centre would make the math a lot more complicated.

The fluid solution describes the spacetime within an enclosed volume that has none zero density. The density of black hole at the centre can be analysed simply as the mass of the black hole enclosed in a spherical volume defined by the Schwarzschild radius of that black hole. At the Schwarzschild radius of the black hole the gravitational time dilation at that radius is completely independent of how the mass is distributed within the enclosing volume. Whether you consider all the mass to to be enclosed in zero volume at the centre of the black hole or evenly distributed throughout the Schwarzschild radius volume the solution at the Schwarzschild radius is the same as long as the distribution is rotationally symmetric. The interior solution requires that in order to calculate the gravitational time dilation at any radius that you take into account the mass inside that radius and the non enclosed mass outside that radius. The simplest way to do this analysis is take the total mass of the swarm stars and assume that total mass is evenly distributed in the volume outside the central black hole. It is also relatively simple to analyse the case where the mass density is not evenly distributed as long as there is a simple relationship between radius and density and as long as rotational symmetry is maintained. For example to analyse the spacetime of an Earth like planet that is non rotating and contained in an otherwise empty universe, then you could divide it up into convenient concentric shells such as core, mantle, crust and atmosphere and analyse it using the interior solution and for the vacuum above the atmsphere you would use the exterior solution and come up with a model that is a reasonable aproximate description of the spacetime.

In the case of the star swarm, if the further simplifying assumption that the system is reasonably static is made, then the time dilation at the Schwarzschild radius of the enclosed black hole can be calculated and shown to be none zero.

However, the assumption that the system is static, is a big and admittedly over simplifying assumption and the changing density of the system due to the moving mass of the radially infalling swarm stars will make a significant difference to the calculations when that is taken into account. If we take the accepted conclusion that all mass within the Schwarzschild radius of a system ends up at the centre of the system it seems reasonable to assume that the final stable condition of any system is one with a single event horizon. By not too great a leap of imagination, it is probably reasonable to assume that the laws of nature conspire to ensure that one event horizon enclosed within another is an unstable and very temporary (and possibly impossible) situation in a non rotating system.

Anyway, what is your proposed solution and conclusion?

Nothing forbids the presence of an horizon inside a black hole, however it cannot be an event horizon by definition. But you could find another definition for it, such as a future outer trapping horizon.

In the above post you seem to be agreeing that it is not possible to have one event horizon enclosed within another event horizon so I am not sure why you seem to be disagreeing with me in the other posts.

If we have one black hole within another black hole and the enclosed black hole does not have its own event horizon then would you agree that the enclosed black hole is probably not what we would call a black hole. Here I am using my interpretation of the definition of a black hole as something that has its own event horizon. If an object does not have an event horizon then its does not have a very strong claim to being called a black hole.

A swarm of stars would be loosely described by the interior Schwarzschild solution if you make the aproximation that the mass is distributed evenly rather than concentrated in the stars. The FRW metric for the universe as a whole makes a similar sort of aproximation that the mass of galaxies is evenly spread out in space and ignores the fact that most of the mass is actually highly concentrated in localised regions.

The Schwarzschild and FRW solutions give completely different effects.

I never claimed that they gave the same effect. I was simply making the observation that in physics we generally make the analysis a bit simpler by making assumptions such as homogenuity when we know that is the reality. For instance in Newtonian gravity when we say the acceleration of gravity at the surface of the Earth is GM/R^2 we make the impicit assumption that the Earth is spherical with no hills and valleys and that the mass is evenly distributed, even though we know that is not the case. Doing the calculations taking every tree and blade of grass into account becomes tedious. That does not imply that I am saying that Newtonian gravity gives the same effect as the FRW solution. I was just talking about the use of aproximations in physics generally.

As for the FRW metric some people claim the assumption of homogenuity is an over simplification with significant errors when you take into account that mass in the universe is concentrated in galaxies and that there are large scale structures such as galaxy clusters, sheets and filaments sometimes interspersed with vast voids.

However, the main difference between the interior Schwarzschild solution and the FRW metric is the the former is a static solution and the latter is not. In fact that possibly makes the FRW metric a better method to analyse the swarm of stars.

A swarm of stars would be loosely described by the interior Schwarzschild solution if you make the aproximation that the mass is distributed evenly rather than concentrated in the stars.

Is that a conclusion that is drawn from GR or just your guess?

That is the conclusion I have drawn from GR so you could call it my guess. I said "loosely" because the interior solution is static and swarm of stars is not. So you would have to assume a short interval of time and infalling radial velocities that are small relative to the volume and time interval under considertion. It is a bit like assuming Special Relativity applies in a very small (possibly infintesimal) volume of curved spacetime.

The important point of my previous posts, as I mentioned to Xantox, is that the interior Schwarzschild fluid solution is a better method to analyse the swarm of stars than the normal exterior Schwarzschild vacuum solution. Do you agree?

Earlier you agreed with Xantox that the Schwarzschild solution only applies to empty space. Do you acknowledge that is not a true statement, when I was specifically talking about the interior Schwarzschild solution?

 

[xantox]

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).

 

[yuiop]

... (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.

...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...

 

[Phrak]

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 referring to the singularity of the large black hole, or an additional black hole that fell in?

 

[yuiop]

kev. Perhaps you could back up and explain what you mean by a black hole at the centre.
Are you referring to the singularity of the large black hole, or an additional black hole that fell in?

I meant an additional independent fully formed black hole 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 Schwarzschild 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 Schwarzschild 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 Schwarzschild 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).

 

[Phrak]

I meant an additional independent fully formed black hole 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 Schwarzschild 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 Schwarzschild 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 Schwarzschild 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).

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?

 

[xantox]

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).

 

[Phrak]

...(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.

 

[Max™]

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.

 

[xantox]

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.

 

[Haelfix]

The problem with having a black hole inside a black hole 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 black hole/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.

 

[Phrak]

Worse, there is a problem with the asymptotics. The asymptotics of the interior black hole/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 black hole??

If that's what your claiming, that's 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.

 

[hurk4]

Concepts of time and space cease to be meaningful inside the event horizon of a black hole.

Unless someone is inside a BH??

 

[George Jones]

Unless someone is inside a BH??

Look at the reply, post #6, by xantox.

 

[JohnnyBoy]

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

 

[rkyeun]

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.

 

[MathematicalPhysicist]

The problem with having a black hole inside a black hole 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 black hole/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?

Excuse me bumping this thread.