Symmetric non-expanding horizons

Abstract

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.

Revtex4, 36 pages

References in corpus (2)

• Geometry of null hypersurfaces
• Local approach to thermodynamics of black holes

Cited by in corpus (3)

• Isolated, slowly evolving, and dynamical trapping horizons: geometry and mechanics from surface deformations
• Black holes and black hole thermodynamics without event horizons
• Quasi--local angular momentum of non--symmetric isolated and dynamical horizons from the conformal decomposition of the metric