Abstract
We prove that, under certain conditions, the topology of the event horizon of a four-dimensional asymptotically flat black-hole spacetime must be a 2-sphere. No stationarity assumption is made. However, in order for the theorem to apply, the horizon topology must be unchanging for long enough to admit a certain kind of cross section. We expect this condition is generically satisfied if the topology is unchanging for much longer than the light-crossing time of the black hole. More precisely, let M be a four-dimensional asymptotically flat spacetime satisfying the averaged null energy condition, and suppose that the domain of outer communication to the future of a cut K of is globally hyperbolic. Suppose further that a Cauchy surface for is a topological 3-manifold with compact boundary in M, and is a compact submanifold of with spherical boundary in (and possibly other boundary components in ). Then we prove that the homology group must be finite. This implies that either consists of a disjoint union of 2-spheres, or is non-orientable and contains a projective plane. Furthermore, , and will be a cross section of the horizon as long as no generator of becomes a generator of . In this case, if is orientable, the horizon cross section must consist of a disjoint union of 2-spheres.
| Original language | English (US) |
|---|---|
| Article number | 012 |
| Pages (from-to) | 1055-1061 |
| Number of pages | 7 |
| Journal | Classical and Quantum Gravity |
| Volume | 12 |
| Issue number | 4 |
| DOIs | |
| State | Published - 1995 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Physics and Astronomy(all)
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Topology of event horizons and topological censorship. / Jacobson, Ted; Venkataramani, Shankar C.
In: Classical and Quantum Gravity, Vol. 12, No. 4, 012, 1995, p. 1055-1061.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Topology of event horizons and topological censorship
AU - Jacobson, Ted
AU - Venkataramani, Shankar C
PY - 1995
Y1 - 1995
N2 - We prove that, under certain conditions, the topology of the event horizon of a four-dimensional asymptotically flat black-hole spacetime must be a 2-sphere. No stationarity assumption is made. However, in order for the theorem to apply, the horizon topology must be unchanging for long enough to admit a certain kind of cross section. We expect this condition is generically satisfied if the topology is unchanging for much longer than the light-crossing time of the black hole. More precisely, let M be a four-dimensional asymptotically flat spacetime satisfying the averaged null energy condition, and suppose that the domain of outer communication to the future of a cut K of is globally hyperbolic. Suppose further that a Cauchy surface for is a topological 3-manifold with compact boundary in M, and is a compact submanifold of with spherical boundary in (and possibly other boundary components in ). Then we prove that the homology group must be finite. This implies that either consists of a disjoint union of 2-spheres, or is non-orientable and contains a projective plane. Furthermore, , and will be a cross section of the horizon as long as no generator of becomes a generator of . In this case, if is orientable, the horizon cross section must consist of a disjoint union of 2-spheres.
AB - We prove that, under certain conditions, the topology of the event horizon of a four-dimensional asymptotically flat black-hole spacetime must be a 2-sphere. No stationarity assumption is made. However, in order for the theorem to apply, the horizon topology must be unchanging for long enough to admit a certain kind of cross section. We expect this condition is generically satisfied if the topology is unchanging for much longer than the light-crossing time of the black hole. More precisely, let M be a four-dimensional asymptotically flat spacetime satisfying the averaged null energy condition, and suppose that the domain of outer communication to the future of a cut K of is globally hyperbolic. Suppose further that a Cauchy surface for is a topological 3-manifold with compact boundary in M, and is a compact submanifold of with spherical boundary in (and possibly other boundary components in ). Then we prove that the homology group must be finite. This implies that either consists of a disjoint union of 2-spheres, or is non-orientable and contains a projective plane. Furthermore, , and will be a cross section of the horizon as long as no generator of becomes a generator of . In this case, if is orientable, the horizon cross section must consist of a disjoint union of 2-spheres.
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UR - http://www.scopus.com/inward/citedby.url?scp=33845599328&partnerID=8YFLogxK
U2 - 10.1088/0264-9381/12/4/012
DO - 10.1088/0264-9381/12/4/012
M3 - Article
AN - SCOPUS:33845599328
VL - 12
SP - 1055
EP - 1061
JO - Classical and Quantum Gravity
JF - Classical and Quantum Gravity
SN - 0264-9381
IS - 4
M1 - 012
ER -