Abstract
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 × 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).
| Original language | English (US) |
|---|---|
| Pages (from-to) | 571-576 |
| Number of pages | 6 |
| Journal | Communications in Mathematical Physics |
| Volume | 266 |
| Issue number | 2 |
| DOIs | |
| State | Published - Sep 2006 |
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ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics
Cite this
A generalization of Hawking's black hole topology theorem to higher dimensions. / Galloway, Gregory J; Schoen, Richard.
In: Communications in Mathematical Physics, Vol. 266, No. 2, 09.2006, p. 571-576.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A generalization of Hawking's black hole topology theorem to higher dimensions
AU - Galloway, Gregory J
AU - Schoen, Richard
PY - 2006/9
Y1 - 2006/9
N2 - 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 × 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).
AB - 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 × 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).
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UR - http://www.scopus.com/inward/citedby.url?scp=33746214630&partnerID=8YFLogxK
U2 - 10.1007/s00220-006-0019-z
DO - 10.1007/s00220-006-0019-z
M3 - Article
AN - SCOPUS:33746214630
VL - 266
SP - 571
EP - 576
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 2
ER -