Next-to-leading term of the renormalized stress-energy tensor of the quantized massive scalar field in Schwarzschild spacetime. The back reaction

TL;DR

This paper derives the next-to-leading order correction to the stress-energy tensor of a quantized massive scalar field in Schwarzschild spacetime, providing insights into quantum back reaction effects on black holes.

Contribution

It introduces a method to compute the next-to-leading term of the renormalized stress-energy tensor using the DeWitt-Schwinger effective action and Hadamard coefficients.

Findings

Explicit expression for the next-to-leading term of the stress-energy tensor.

Discussion of quantum back reaction effects on Schwarzschild black holes.

Abstract

The next-to-leading term of the renormalized stress-energy tensor of the quantized massive field with an arbitrary curvature coupling in the spacetime of the Schwarzschild black hole is constructed. It is achieved by functional differentiation of the DeWitt-Schwinger effective action involving coincidence limit of the Hadamard-Minakshisundaram-DeWitt-Seely coefficients $a_{3}$ and $a_{4}.$ The back reaction of the quantized field upon the Schwarzschild black hole is briefly discussed.