Approximate stress-energy tensor of the massless spin-1/2 field in Schwarzschild spacetime

TL;DR

This paper constructs an approximate stress-energy tensor for a massless spin-1/2 field in Schwarzschild spacetime, showing good agreement with numerical results and discussing its back reaction on the metric.

Contribution

It provides a new approximate analytical form of the stress-energy tensor for the massless spin-1/2 field in Schwarzschild spacetime, validated against numerical calculations.

Findings

The constructed tensor agrees well with numerical data.

The method ensures conservation and regularity conditions.

Back reaction effects are briefly discussed.

Abstract

The approximate stress-energy tensor of the conformally invariant massless spin-1/2 field in the Hartle-Hawking state in the Schwarzschild spacetime is constructed. It is shown that by solving the conservation equation in conformal space and utilizing the regularity conditions in a physical metric one obtains the stress-energy tensor that is in a good agreement with the numerical calculations. The back reaction of the quantized field upon the spacetime metric is briefly discussed.