Black Hole Radiation (with and) without Weyl Anomaly

TL;DR

This paper investigates how different measures in path integral quantization affect black hole radiation in dilaton gravity, revealing that despite the Weyl anomaly's dependence on a parameter, the observed radiation remains unaffected.

Contribution

It introduces a one-parameter family of measures in the path integral approach and shows the invariance of black hole radiation against this parameter.

Findings

Weyl anomaly is proportional to the parameter k

Black hole radiation at future null infinity is independent of k

Radiation results are robust against measure variations

Abstract

In the semiclassical analysis of black hole radiation in matter-coupled dilaton gravity, a one-parameter ``$k$"-family of measures for the path integral quantization of the matter fields is considered. The Weyl anomaly is proportional to the parameter $k$, but the black hole radiation seen by minkowskian observers at future null infinity is $k$-independent.