Horizon surface gravity as 2 d geodesic expansion

@inproceedings{JacobsonHorizonSG,
  title={Horizon surface gravity as 2 d geodesic expansion},
  author={Ted Jacobson and Renaud Parentani}
}
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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