Generalization of the "Schwarzschild surface" to arbitrary static and stationary metrics

Abstract

A generalization of the r = 2m "Schwarzschild surface'' is defined for static metrics which are not necessarily spherically symmetric. This surface exhibits simultaneously the properties of being a "one-way membrane'' for causal propagation and of being a surface of infinite red shift. The necessary and sufficient condition that these two phenomena take place on the same surface in an arbitrary stationary metric is also obtained. The distinctions between the static and stationary cases are shown to be essential by examples from the Kerr metric.