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.
Highlights
The renormalized expectation value of the stress-energy tensor operator (RSET) hTμνiren of a quantum field is a quantity of primary interest in quantum field theory in curved spacetime
We have studied quantum field theory on pure anti–de Sitter (adS) with general mixed (Robin) boundary conditions applied to the field [77]
Inspired by our recent work on the effect of boundary conditions on quantum field theory in pure adS [77], in this paper we extend our previous study of the vacuum polarization (VP) on topological black holes [68] by considering general mixed (Robin) boundary conditions
Summary
The renormalized expectation value of the stress-energy tensor operator (RSET) hTμνiren of a quantum field is a quantity of primary interest in quantum field theory in curved spacetime. Hiscock and Samuel (AHS) [17,18] developed a general methodology for computing both the VP and RSET for a quantum scalar field with arbitrary mass and coupling to the spacetime curvature, on a static, spherically symmetric black hole background. Inspired by our recent work on the effect of boundary conditions on quantum field theory in pure adS [77], in this paper we extend our previous study of the VP on topological black holes [68] by considering general mixed (Robin) boundary conditions. Using the methodology developed in [68], we compute the renormalized VP for a massless, conformally coupled scalar field on a variety of black holes with spherical, flat and hyperbolic horizons, paying particular attention to the effect of changing the boundary conditions satisfied by the scalar field.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
