The Double-Copy Root of Hawking Thermality

TL;DR

This paper investigates Hawking radiation from a collapsing shell through the non-abelian Yang-Mills root of the gravitational double copy. It develops an eikonal S-matrix framework in a Kerr-Schild/Vaidya background to derive the color-resolved radiation spectrum. The main finding is that the spectrum is thermal in the color eigenvalue $\lambda$, with the differential color spectrum $dN/d\lambda \propto \left( \frac{C\lambda}{\sinh(\pi C\lambda)} \right) \sqrt{R^2-\lambda^2}$, where $\rho(\lambda)$ is the Wigner semicircle density; gravity inherits a Planck-like energy spectrum because $\beta(\lambda)$ is linear in $E$ in the root construction. This work reframes gravitational thermality as dual to color thermality in gauge theory, linking black-hole thermodynamics to soft-gluon dynamics in the YM root, and suggests a broader role for the double copy in black-hole microphysics.

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 $λ$, not energy. Considering the $SU(N_c)$ gauge theory in the large $N_c$ limit, we find the differential spectrum $dN/ dλ$ 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.

Figures (1)

• Figure 1: The spectrum of radiated color charge, $\mathrm{d} N/\mathrm{d} \lambda$, for fixed radius $R=1$ and varying effective coupling $C$. As $C$ increases, the spectrum transitions from the phase-space-dominated Wigner semicircle to a dynamically-dominated thermal distribution.