Conformal Invariance of Black Hole Temperature

TL;DR

This paper demonstrates that the temperature of stationary black holes remains invariant under certain conformal transformations, providing a new conformal invariant definition of surface gravity that aligns with Hawking radiation.

Contribution

It introduces a conformal invariant definition of surface gravity for conformal Killing horizons, extending the understanding of black hole thermodynamics under conformal transformations.

Findings

Surface gravity and temperature are conformally invariant for stationary black holes.

The new definition agrees with traditional ones for Killing horizons.

Reconciliation of trace anomaly behavior with Hawking radiation under conformal changes.

Abstract

It is shown that the surface gravity and temperature of a stationary black hole are invariant under conformal transformations of the metric that are the identity at infinity. More precisely, we find a conformal invariant definition of the surface gravity of a conformal Killing horizon that agrees with the usual definition(s) for a true Killing horizon and is proportional to the temperature as defined by Hawking radiation. This result is reconciled with the intimate relation between the trace anomaly and the Hawking effect, despite the {\it non}invariance of the trace anomaly under conformal transformations.