Horizon surface gravity as 2d geodesic expansion

Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology

Scientific paper

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Additional info

7 pages; v2: 8 pages, derivation of (8) in section 3 streamlined, added new expression for the 2d expansion, minor editing

Type

Scientific paper

Digital Object Identifier

10.1088/0264-9381/25/19/195009

Abstract

The surface gravity of any Killing horizon, in any spacetime dimension, can
be interpreted as a local, two-dimensional expansion rate seen by freely
falling observers when they cross the horizon. Any two-dimensional congruence
of geodesics invariant under the Killing flow can be used to define this
expansion, provided that the observers have unit Killing energy.

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