The Double-Copy Root of Hawking Thermality

TL;DR

This paper shows that Hawking radiation's thermal spectrum can be derived from a gauge theory perspective, revealing a duality between energy thermality in gravity and charge thermality in gauge theories, using the double copy approach.

Contribution

It introduces a novel gauge theory derivation of Hawking radiation, linking the thermal spectrum to the color charge eigenvalues and employing random matrix theory for the gauge side.

Findings

The radiation spectrum is thermal in the color charge eigenvalue, not energy.

The differential spectrum combines a Planck-like factor with a Wigner semicircle distribution.

Energy thermality in gravity corresponds to charge thermality in gauge theory.

Abstract

The Hawking radiation spectrum from a collapsing null shell can be derived via the double copy of a simpler gauge theory calculation. Analyzing the non-abelian Yang-Mills root of this process, we demonstrate that the radiation spectrum is thermal in the color charge eigenvalue $\lambda$, not energy. Considering the $SU(N_c)$ gauge theory in the large $N_c$ limit, we find the differential spectrum $dN/ d\lambda$ is a product of the gravitationally familiar Planck-like factor and the color phase space density, modeled here as the Wigner semicircle from random matrix theory. This reveals that apparent energy thermality in gravity is the direct dual of charge thermality in its underlying non-abelian gauge theory.