Horizon surface gravity as 2d geodesic expansion

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

References in corpus (4)

• Analogue Gravity
• Trans-Planckian redshifts and the substance of the space-time river
• Black Holes in the Ghost Condensate
• Bumpy black holes from spontaneous Lorentz violation

Cited by in corpus (7)

• Mechanics of universal horizons
• Surface gravities for non-Killing horizons
• From vacuum fluctuations across an event horizon to long distance correlations
• Black holes and Hawking radiation in spacetime and its analogues
• Dispersive fields in de Sitter space and event horizon thermodynamics
• The Basics of Water Waves Theory for Analogue Gravity
• Surface gravity from tidal acceleration