Extrinsic time formalism for the Euclidean black hole in a box.

Abstract

We return to the problem of Euclidean black holes in thermodynamical equilibrium with radiation, under the conditions of the statistical mechanical canonical ensemble. This time we use Kucha\ifmmode \check{r}\else \v{r}\fi{}'s ``extrinsic time'' formalism in order to select the set of true dynamical variables. With this set of canonical variables, {R\ifmmode \tilde{}\else \~{}\fi{},${\mathit{P}}_{\mathit{R}\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}}$,M,${\mathit{P}}_{\mathit{M}}$}, and York's proposal for the boundary and ``horizon'' terms, we compute a classically consistent total action for the Euclidean black hole. We show explicitly that the ``zero-loop'' partition function derived from this total action is identical to the one already in the literature of this area. \textcopyright{} 1996 The American Physical Society.