- #1

martinbn

Science Advisor

- 2,215

- 745

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter martinbn
- Start date

- #1

martinbn

Science Advisor

- 2,215

- 745

- #2

- 31,070

- 7,753

- #3

martinbn

Science Advisor

- 2,215

- 745

That is different, I am not asking about the topology of the space-time, just a cross section of the event horizon.

I found this [PLAIN]http://arxiv.org/abs/gr-qc/9410004[/PLAIN] [Broken]

http://arxiv.org/abs/gr-qc/9410004

which is relevant, but my questions remain.

I found this [PLAIN]http://arxiv.org/abs/gr-qc/9410004[/PLAIN] [Broken]

http://arxiv.org/abs/gr-qc/9410004

which is relevant, but my questions remain.

Last edited by a moderator:

- #4

- 31,070

- 7,753

##S^2 \times R## or just ##S^2## depending on what you mean.

If you mean some other spacetime than a Schwarzschild spacetime then I don't know what you mean by "black hole"

If you mean some other spacetime than a Schwarzschild spacetime then I don't know what you mean by "black hole"

Last edited:

- #5

Ben Niehoff

Science Advisor

Gold Member

- 1,879

- 162

In 4d, one can prove (as you have found) that the horizon is spherical. However, this proof works only in 4d. In higher dimensions, one can find other topologies, the simplest example being "black rings" in 5d, which have horizon topology ##S^2 \times S^1## (as opposed to ##S^3## for spherical black holes). I seem to remember that the general proof shows that the horizon is a manifold of positive Yamabe invariant, or something like that.

- #6

martinbn

Science Advisor

- 2,215

- 745

Share: