Vacuum polarization on topological black holes with Robin boundary conditions

TL;DR

This paper calculates the quantum vacuum polarization for a scalar field around anti-de Sitter black holes with various horizon topologies under Robin boundary conditions, revealing boundary condition effects on the vacuum state.

Contribution

It provides the first detailed computation of vacuum polarization with Robin boundary conditions on topological black holes in AdS space.

Findings

Vacuum polarization approaches a finite limit far from the black hole.

Boundary conditions significantly influence the vacuum polarization near the boundary.

Results are consistent across different horizon topologies except for Dirichlet conditions.

Abstract

We compute the renormalized vacuum polarization for a massless, conformally coupled scalar field on asymptotically anti-de Sitter black hole backgrounds. Mixed (Robin) boundary conditions are applied on the spacetime boundary. We consider black holes with nonspherical event horizon topology as well as spherical event horizons. The quantum scalar field is in the Hartle-Hawking state, and we employ Euclidean methods to calculate the renormalized expectation values. Far from the black hole, we find that the vacuum polarization approaches a finite limit, which is the same for all boundary conditions except Dirichlet boundary conditions.