Horizon surface gravity as 2d geodesic expansion

TL;DR

This paper proposes a novel interpretation of horizon surface gravity as a local 2D geodesic expansion rate experienced by freely falling observers crossing a Killing horizon, applicable in any spacetime dimension.

Contribution

It introduces a new geometric perspective linking surface gravity to 2D geodesic expansion, generalizing previous concepts across dimensions.

Findings

Surface gravity equals 2D geodesic expansion rate.

Applicable to any spacetime dimension.

Defines expansion via invariant geodesic congruences.

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.