Hawking Radiation meets the Double Copy

TL;DR

The paper embeds Hawking radiation in the double-copy framework by constructing a gauge-theory analogue through the single copy of a collapsing spacetime, the sqrt-Vaidya background. Using an all-orders eikonal resummation of ladder diagrams and a semiclassical ray-tracing check, it derives explicit Bogoliubov amplitudes A(E,E0) and B(E,E0) that govern particle production. It reveals an energy-independent number spectrum controlled by the dimensionless coupling α = QQ_B/(4π), and interprets this in terms of fugacity rather than temperature within the double-copy context. These results provide a concrete gauge-theory route to semi-classical black-hole radiation and point to avenues for extending the double-copy correspondence to dynamical spacetimes and beyond.

Abstract

We describe an electromagnetic system which is related to black hole production with Hawking radiation through the double copy. We consider the scattering of a massless scalar particle through a collapsing electromagnetic background -- the single copy of Vaidya -- and identify the Feynman diagrams that exponentiate in the geometric-optics limit. The Bogoliubov coefficients obtained from the diagrammatic approach are reproduced by a semiclassical ray-tracing computation of null rays in this same background. We discuss the thermodynamic interpretation of the resulting number distribution in light of the double copy.

Figures (1)

• Figure 1: Scattering on a $\sqrt{\rm Vaidya}$ (Vaidya) background on the left (right) figure. In the $\sqrt{\rm Vaidya}$ case, the infalling shell of radiation creates a charge at $t+r=0$, we set our initial state to be inside this infalling shell (unshaded region). For the Vaidya case, the infalling shell of radiation creates a black hole at $t+r=0$ (shaded region). In Aoude:2024sve, the authors considered initial states with $t+r<-4GM$ that do not fall inside the horizon.