A quantitative version of Hawking radiation

TL;DR

This paper provides a rigorous, quantitative proof of Hawking radiation for massive bosons in Schwarzschild-de Sitter spacetime, including decay rate estimates and a non-spherical symmetry approach.

Contribution

It introduces a novel, quantitative proof of Hawking radiation that does not depend on spherical symmetry and includes decay estimates for the quantum state.

Findings

Established the existence of Hawking radiation for massive bosons.

Provided decay rate estimates for the quantum state.

Developed a non-spherical symmetry proof approach.

Abstract

We present a proof of the existence of the Hawking radiation for massive bosons in the Schwarzchild-de Sitter metric. It provides estimates for the rates of decay of the initial quantum state to the Hawking thermal state. The arguments in the proof include a construction of radiation fields by conformal scattering theory; a semiclassical interpretation of the blueshift effect; and the use of a WKB parametrix near the surface of a collapsing star. The proof does not rely on the spherical symmetry of the spacetime.