### Abstract

A key result in four-dimensional black hole physics, since the early 1970s, is Hawking's topology theorem assertion that the cross-sections of an 'apparent horizon', separating the black hole region from the rest of the spacetime, are topologically 2-spheres. Later, during the 1990s, by applying a variant of Hawking's argument, Gibbons and Woolgar could also show the existence of a genus-dependent lower bound for the entropy of topological black holes with negative cosmological constant. Recently, Hawking's black hole topology theorem, along with the results of Gibbons and Woolgar, has been generalized to the case of black holes in higher dimensions. Our aim here is to give a simple self-contained proof of these generalizations, which also makes their range of applicability transparent.

Original language | English |
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Article number | 162001 |

Journal | Classical and Quantum Gravity |

Volume | 25 |

Issue number | 16 |

DOIs | |

Publication status | Published - Aug 21 2008 |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

**A simple proof of the recent generalizations of Hawking's black hole topology theorem.** / Rácz, I.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - A simple proof of the recent generalizations of Hawking's black hole topology theorem

AU - Rácz, I.

PY - 2008/8/21

Y1 - 2008/8/21

N2 - A key result in four-dimensional black hole physics, since the early 1970s, is Hawking's topology theorem assertion that the cross-sections of an 'apparent horizon', separating the black hole region from the rest of the spacetime, are topologically 2-spheres. Later, during the 1990s, by applying a variant of Hawking's argument, Gibbons and Woolgar could also show the existence of a genus-dependent lower bound for the entropy of topological black holes with negative cosmological constant. Recently, Hawking's black hole topology theorem, along with the results of Gibbons and Woolgar, has been generalized to the case of black holes in higher dimensions. Our aim here is to give a simple self-contained proof of these generalizations, which also makes their range of applicability transparent.

AB - A key result in four-dimensional black hole physics, since the early 1970s, is Hawking's topology theorem assertion that the cross-sections of an 'apparent horizon', separating the black hole region from the rest of the spacetime, are topologically 2-spheres. Later, during the 1990s, by applying a variant of Hawking's argument, Gibbons and Woolgar could also show the existence of a genus-dependent lower bound for the entropy of topological black holes with negative cosmological constant. Recently, Hawking's black hole topology theorem, along with the results of Gibbons and Woolgar, has been generalized to the case of black holes in higher dimensions. Our aim here is to give a simple self-contained proof of these generalizations, which also makes their range of applicability transparent.

UR - http://www.scopus.com/inward/record.url?scp=56349104568&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=56349104568&partnerID=8YFLogxK

U2 - 10.1088/0264-9381/25/16/162001

DO - 10.1088/0264-9381/25/16/162001

M3 - Article

AN - SCOPUS:56349104568

VL - 25

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 16

M1 - 162001

ER -