A generalization of Hawking's black hole topology theorem to higher dimensions

Details A generalization of Hawking's black hole topology theorem to higher dimensions A generalization of Hawking's black hole topology theorem to higher dimensions

2005-09-27

arxiv.org/abs/gr-qc/0509107v2

Commun.Math.Phys. 266 (2006) 571-576

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages, latex2e, references updated, minor corrections, to appear in Communications in Mathematical Physics

Scientific paper

10.1007/s00220-006-0019-z

Hawking's theorem on the topology of black holes asserts that cross sections of the event horizon in 4-dimensional asymptotically flat stationary black hole spacetimes obeying the dominant energy condition are topologically 2-spheres. This conclusion extends to outer apparent horizons in spacetimes that are not necessarily stationary. In this paper we obtain a natural generalization of Hawking's results to higher dimensions by showing that cross sections of the event horizon (in the stationary case) and outer apparent horizons (in the general case) are of positive Yamabe type, i.e., admit metrics of positive scalar curvature. This implies many well-known restrictions on the topology, and is consistent with recent examples of five dimensional stationary black hole spacetimes with horizon topology $S^2 \times S^1$. The proof is inspired by previous work of Schoen and Yau on the existence of solutions to the Jang equation (but does not make direct use of that equation).

Affiliated with

Also associated with

No associations

Rating

A generalization of Hawking's black hole topology theorem to higher dimensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A generalization of Hawking's black hole topology theorem to higher dimensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A generalization of Hawking's black hole topology theorem to higher dimensions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-224563