Some general properties of the renormalized stress-energy tensor for static quantum states on (n+1)-dimensional spherically symmetric black holes

TL;DR

This paper derives conditions for the regularity of the renormalized stress-energy tensor in static quantum states on higher-dimensional spherically symmetric black holes, providing a general framework for future calculations across dimensions.

Contribution

It presents a method to express the RSET in terms of a single unknown function and arbitrary constants, with conditions for regularity at horizons in any number of dimensions.

Findings

Derived the RSET in terms of a single function and constants.

Established regularity conditions at event horizons including extremal cases.

Provided a framework applicable to any number of space-time dimensions.

Abstract

We study the renormalized stress-energy tensor (RSET) for static quantum states on (n+1)-dimensional, static, spherically symmetric black holes. By solving the conservation equations, we are able to write the stress-energy tensor in terms of a single unknown function of the radial co-ordinate, plus two arbitrary constants. Conditions for the stress-energy tensor to be regular at event horizons (including the extremal and ``ultra-extremal'' cases) are then derived using generalized Kruskal-like co-ordinates. These results should be useful for future calculations of the RSET for static quantum states on spherically symmetric black hole geometries in any number of space-time dimensions.