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 Schwarzchild 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 Schwarzchild 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

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

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

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

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

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 blackhole taking a smaller blackhole 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 blackhole?

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.

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

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.

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

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

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 Schwarzchild 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

The Schwarzschild and FRW solutions give completely different effects.

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

xantox

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?