Fluctuation-Dissipation relation from anomalous stress tensor and Hawking effect

TL;DR

This paper establishes a universal connection between the fluctuation-dissipation relation and Hawking radiation, deriving black hole temperature from anomalous stress tensor correlators in any dimension.

Contribution

It demonstrates that the fluctuation-dissipation relation applies to black hole horizons using gravitational anomalies, linking microscopic fluctuations to Hawking temperature.

Findings

Correlators satisfy the Kubo relation for black hole horizons.

Black hole temperature is derived from stress tensor fluctuations.

Reproduces Tolman and Hawking temperatures from anomaly-based correlators.

Abstract

We show a direct connection between Kubo's fluctuation-dissipation relation and Hawking effect that is valid in any dimensions for any stationary or static black hole. The relevant correlators corresponding to the fluctuating part of the force, computed from the known expressions for the anomalous stress tensor related to gravitational anomalies, are shown to satisfy the Kubo relation, from which the temperature of a black hole as seen by an observer at an arbitrary distance is abstracted. This reproduces the Tolman temperature and hence the Hawking temperature as that measured by an observer at infinity.