History of a black hole horizon.

*(English)*Zbl 1308.83078Summary: The most dynamic changes in a black hole horizon occur as the black hole is forming and before it settles into a stationary state. The definition of the event horizon and the properties of null hypersurfaces imply that the horizon is generated by null geodesics, which enter the horizon at a “crease set”. This acausal and typically 2-dimensional and finite set can be regarded as the horizon’s origin. But in a physically motivated time sequence the horizon starts at a lower-dimensional subset of the crease set and can assume various topologies during its history, depending on how the time sequence slices up the spacetime, and on the possible branchings of the crease set. An alternative description of the horizon propagates it backwards in time from its spherical shape at large times through self-intersecting surfaces, which can represent topological changes smoothly. A number of examples are given, which illustrate some of the possible changes in the horizon’s early history.

Reviewer: Reviewer (Berlin)

##### MSC:

83C57 | Black holes |

83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |

83C75 | Space-time singularities, cosmic censorship, etc. |

54F65 | Topological characterizations of particular spaces |

##### Software:

AHFinderDirect
Full Text:
DOI

##### References:

[1] | Fish, V L; Doeleman, S S, Observing a black hole event horizon: (sub)millimeter VLBI of sgr A*, Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis, Proc. Int. Astron. Union, IAU Symposium, 261, 271, (2010) |

[2] | K. S. Thorne et al., Black Holes: the Membrane Paradigm (Yale, 1986). · Zbl 1374.83002 |

[3] | Anninos, P; etal., Dynamics of apparent and event horizons, Phys. Rev. Lett., 74, 630, (1995) |

[4] | Siino, M, Topological appearance of event horizon, Prog. Theor. Phys., 99, 1, (1998) |

[5] | J. Thornburg, Event and Apparent Horizon Finders for 3+1 Numerical Relativity, Sect 5.3, http://relativity.livingreviews.org/open?pubNo=lrr-2007-3. · Zbl 1116.83001 |

[6] | Israel, W, No article title, Nuovo Cim., 44B, 1, (1966) |

[7] | Oppenheimer, J R; Snyder, H, On continued gravitational contraction, Phys. Rev., 56, 455, (1939) · Zbl 0022.28104 |

[8] | Brill, D; Khetarpal, P; Kaul, V, No article title, Pramana, 69, 109, (2007) |

[9] | Matzner, R A; etal., No article title, Geometry of a black hole collision, Science, 270, 941, (1995) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.