Hollow spherical blackhole thought experiment

[Instine]

Right - I've set up a https://www.physicsforums.com/showthread.php?t=124970".

Not had/got time to give much of an answer yet, but more will come.

 

[coalquay404]

Apologies for digging this thread up after so long. However, on reading Crother's posts, it's clear that he misunderstands some reasonably elementary concepts behind exact analytic solutions to the field equations. That said, he does make a reasonably exact point about multiple black hole solutions to Einstein's equations (although, I suspect, for reasons which are very wrong).

In spite of the impression that many people have, multiple black hole solutions is a reasonably delicate area. There's a copious amount of literature on the subject, all of which is well known, so I won't repeat it here. However, an interesting point is that Einstein's equations *do not* admit multiple black hole solutions in asymptotically flat, vacuum, static spacetimes. There's a huge and interesting selection of research on this area, much of it employing the use of Green's functions at infinity to analyse the spacetime (it also has a very close connection with the Riemannian Penrose inequality, but I digress). The canonical paper on this subject is Non-Existence of Multiple Black Holes in Asymptotically Euclidean Static Vacuum Space-Time, Bunting & Masood-ul-Alam, Gen. Rel. and Grav. 19(2) (1987).

 

[pervect]

However, an interesting point is that Einstein's equations *do not* admit multiple black hole solutions in asymptotically flat, vacuum, static spacetimes.

I'd probably have to special order the reference you quoted. I'm probably not interested enough to spend money on the topic at this point, but I'd be interested in any comments you have about how one tells when solutions are different. Suppose, for instance, we have two solutions, which are related by a diffeomorphism - are they "different", or the "same"?

More to the point,what about the case when a diffeomorphism exists that maps the points of one solution to a subset of the points of another solution? Are the two solutions "different"? How do we express this more exactly?

 

[George Jones]

Hi Pervect, I think you're reading this the way I originally read it, however, coalquay404 is talking about one spacetime in which there are two (or more) black holes, i.e, one solution to Einstein's equation that describes multiple black holes. This is what Crothers talks about in the first paragraph of post #53.

 

[coalquay404]

George Jones is correct. What I was referring to was that one can't develop an exact solution of the field equations which describes a spacetime in which there are two or more black holes. Sorry for the confusion.