$<T^{\mu}_{\nu}>_{ren}$ of the quantized fields in the Unruh state in the Schwarzschild spacetime

TL;DR

This paper constructs the renormalized stress-energy tensor of conformally invariant massless fields in the Unruh state within Schwarzschild spacetime, analyzing its relation to existing approximations.

Contribution

It provides a detailed construction of the renormalized stress-energy tensor in the Unruh state, improving understanding of quantum fields in black hole spacetimes.

Findings

The stress-energy tensor is explicitly constructed using conservation equations and regularity conditions.

The results are compared and related to existing approximation methods.

The approach enhances the accuracy of quantum field predictions near black holes.

Abstract

The renormalized expectation value of the stress energy tensor of the conformally invariant massless fields in the Unruh state in the Schwarzschild spacetime is constructed. It is achieved through solving the conservation equation in conformal space and utilizing the regularity conditions in the physical metric. The relations of obtained results to the existing approximations are analysed.