Extracting Dynamical Degrees of Freedom From the Quasilocal Energy Term in the Gravitational Action

Abstract

It is shown that under proper conditions in an appropriate coordinate system with a suitable time slicing the Einstein-Hilbert action including all necessary boundary terms can be written in terms of the Brown-York quasilocal energy in the absence of matter. If matter is present the non-vanishing bulk term only consists of terms involving the stress-energy tensor. It is argued that the dynamical content of general relativity is stored in the quasilocal energy term. As an example we compute the relevant terms for a modified Vaidya metric which may be used in the investigation of black hole radiance. The bulk term vanishes in the Eddington-Finkelstein kind of coordinate system we use as our preferred gauge with the exception of possible contributions from the stress-energy tensor. Whereas the boundary terms alone are sufficient to cancel second derivatives in the action the presented gauge gives a surface integral of first derivative terms which may be desirable for a quantization of the action, but it is possibly absorbed by the stress-energy contribution to the bulk term.Comment: 6 page