Topological Casimir effect for a class of hyperbolic three-dimensional Clifford-Klein spacetimes

Abstract
The topological Casimir energy for all topologically inequivalent configurations of a massless real scalar field on the hyperbolic three-dimensional Clifford-Klein spacetimes R*H2/ Gamma is evaluated for the case when H2/ Gamma is a compact Riemannian surface of genus g>1. Calculations are performed at both zero and finite temperature with the help of the Selberg trace formula for compact Riemannian surfaces of genus g>1.