Horizon surface gravity as 2d geodesic expansion
arXiv:0806.1677 · doi: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.
7 pages; v2: 8 pages, derivation of (8) in section 3 streamlined, added new expression for the 2d expansion, minor editing