Hadamard Renormalization of the Stress Energy Tensor in a Spherically Symmetric Black Hole Space-Time with an Application to Lukewarm Black Holes

TL;DR

This paper computes the renormalized stress-energy tensor for a quantum field in a spherically symmetric black hole spacetime, applying Hadamard renormalization, with specific results for lukewarm black holes.

Contribution

It introduces a method to calculate the stress-energy tensor in black hole spacetimes using Hadamard renormalization, with explicit results for lukewarm black holes.

Findings

Explicit expressions for the stress tensor components in the exterior region.

Application of the method to lukewarm Reissner-Nordstrom-de Sitter black holes.

Insights into quantum effects near black hole horizons.

Abstract

We consider a quantum field which is in a Hartle-Hawking state propagating in a spherically symmetric black hole space-time. We calculate the components of the stress tensor, renormalized using the Hadamard form of the Green's function, in the exterior region of this space-time. We then specialize these results to the case of the `lukewarm' Riessner-Nordstrom-de Sitter black hole.