Stress Tensor from the Trace Anomaly in Reissner-Nordstrom Spacetimes

TL;DR

This paper presents a method to compute finite quantum stress tensors near Reissner-Nordstrom black hole horizons using the trace anomaly and auxiliary fields, improving upon previous approximations that predicted infinities.

Contribution

It introduces a new approximation scheme based on auxiliary fields that yields finite stress tensors on all RN horizons, including extremal cases, aligning with numerical results.

Findings

Finite stress tensors obtained on all RN horizons.

The scheme reproduces physically consistent quantum behaviors.

Comparison shows improvement over previous infinite stress predictions.

Abstract

The effective action associated with the trace anomaly provides a general algorithm for approximating the expectation value of the stress tensor of conformal matter fields in arbitrary curved spacetimes. In static, spherically symmetric spacetimes, the algorithm involves solving a fourth order linear differential equation in the radial coordinate r for the two scalar auxiliary fields appearing in the anomaly action, and its corresponding stress tensor. By appropriate choice of the homogeneous solutions of the auxiliary field equations, we show that it is possible to obtain finite stress tensors on all Reissner-Nordstrom event horizons, including the extreme Q=M case. We compare these finite results to previous analytic approximation methods, which yield invariably an infinite stress-energy on charged black hole horizons, as well as with detailed numerical calculations that indicate the contrary. The approximation scheme based on the auxiliary field effective action reproduces all physically allowed behaviors of the quantum stress tensor, in a variety of quantum states, for fields of any spin, in the vicinity of the entire family (0 le Q le M) of RN horizons.