Symmetric non-expanding horizons

Details Symmetric non-expanding horizons Symmetric non-expanding horizons

2006-05-04

arxiv.org/abs/gr-qc/0605026v1

Class.Quant.Grav. 23 (2006) 6031-6058

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Revtex4, 36 pages

Scientific paper

10.1088/0264-9381/23/20/022

Symmetric non-expanding horizons are studied in arbitrary dimension. The global properties -as the zeros of infinitesimal symmetries- are analyzed particularly carefully. For the class of NEH geometries admitting helical symmetry a quasi-local analog of Hawking's rigidity theorem is formulated and proved: the presence of helical symmetry implies the presence of two symmetries: null, and cyclic. The results valid for arbitrary-dimensional horizons are next applied in a complete classification of symmetric NEHs in 4-dimensional space-times (the existence of a 2-sphere crossection is assumed). That classification divides possible NEH geometries into classes labeled by two numbers - the dimensions of, respectively, the group of isometries induced in the horizon base space and the group of null symmetries of the horizon.

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