<T^{\mu}_{\nu}>_{ren}> of the quantized conformal fields in the Schwarzschild spacetime: Israel-Hartle-Hawking state

TL;DR

This paper constructs the renormalized stress-energy tensor for conformal fields in Schwarzschild spacetime's Hartle-Hawking state, analyzing its properties and providing semi-analytic models with high accuracy.

Contribution

It introduces a new method for calculating the renormalized stress-energy tensor using conservation equations and regularity conditions, comparing it with Hadamard renormalization.

Findings

Semi-analytic models achieve less than 0.7% deviation in stress tensor components.

The approach clarifies the relation between different renormalization frameworks.

Results enhance understanding of quantum fields in black hole spacetimes.

Abstract

The renormalized expectation value of the stress-energy tensor of the conformally invariant massless field in the Israel-Hartle-Hawking 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. Specifically, the relation of the results of the present approach to the stress tensor constructed within the framework of the Hadamard renormalization is analysed. Finally, the semi-analytic models reconstructing the tangential component of the stress-energy tensor with the maximal deviation not exceeding 0.7% are constructed.