Renormalised vacuum polarisation on topological black holes

Thomas Morley (Sheffield)

5 December 2018

Anti-de Sitter spacetime is a solution of Einstein's equations with a negative cosmological constant. This fact allows for unusual black hole solutions with non-spherical horizon topology.

We calculate the renormalised vacuum polarisation for black holes with spherical, flat and hyperbolic event horizons, following the 'extended coordinates' method, which uses a mode-sum representation for the Hadamard parametrix. Renormalisation counter terms are subtracted from the Green's function mode-by-mode, leaving each individual term manifestly finite.