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Black hole inside a larger black hole. 
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#1
Sep1407, 10:24 AM

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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.



#2
Sep1407, 11:50 AM

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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.



#3
Sep1208, 09:03 AM

P: 56

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 longlasting 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. 


#4
Sep1208, 07:30 PM

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Black hole inside a larger black hole.



#5
Sep1308, 01:35 AM

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



#6
Sep1308, 04:59 AM

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#7
Sep1508, 12:02 AM

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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 hereexcept 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? 


#8
Sep1508, 12:27 AM

P: 2,043

Any references to the literature? 


#9
Sep1508, 05:13 AM

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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 microquasar to the carbonSirius, 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 


#10
Sep1508, 07:03 AM

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#11
Sep1508, 09:29 PM

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"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? 


#12
Sep1508, 11:17 PM

P: 3,967

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. 


#13
Sep1608, 08:29 PM

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#14
Sep1608, 08:51 PM

P: 2,043

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. 


#15
Sep1708, 04:08 AM

P: 3,967

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. 


#16
Sep1708, 11:24 AM

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#17
Sep1708, 12:25 PM

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#18
Sep1708, 08:55 PM

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In your later statement you mention the "fluid solution" which I take as as indirect acknowledgement 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 Schwarzchild radius of that black hole. At the Schwarzchild 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 Schwarzchild 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 Schwarzchild 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? 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. 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 Schwarschild 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. The important point of my previous posts, as I mentioned to Xantox, is that the interior Schwarzchild 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 Schwarschild solution only applies to empty space. Do you acknowledge that is not a true statement, when I was specifically talking about the interior Schwarzchild solution? 


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