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Hawking radiation from the double copy

Anton Ilderton, William Lindved, Karthik Rajeev

TL;DR

The paper addresses how non-perturbative, background-dependent aspects of the gauge–gravity double copy encode black-hole physics, specifically Hawking radiation, by linking a collapsing gauge field to the Vaidya spacetime via the Kerr–Schild double copy. The authors combine worldline methods and amplitude techniques to show that mid-time particle production in a background gauge field double-copies to Hawking radiation in the gravitational collapse, with the double-copy rules $qQ\to M\mathcal{E}$ (or $M\mathcal{E}'$ after a shift) and $g^2\to 2G$ connecting energy changes and eikonal phases across the collapse. They provide an exact gauge-theory calculation of the pair-creation Bogoliubov coefficients using Klein–Gordon modes expressed through Whittaker functions, and demonstrate that in the semiclassical limit these coefficients reproduce the Hawking amplitude and thermal spectrum $T_H=1/(8\pi GM)$. The result unifies several strands of double copy—classical solutions, geodesic conserved quantities, and quantum amplitudes—and suggests avenues for exploring information, backreaction, and Kerr backgrounds within the single-copy framework. Overall, the work highlights how horizon and thermal physics can be encoded in gauge-theory structures and motivates future work on late-time radiation, backreaction, and information-theoretic aspects of the double copy.

Abstract

Gravity and gauge theory are concretely linked by the double copy. Although well-studied at the level of perturbative scattering in vacuum, far less is known about non-perturbative aspects or extensions of the double copy beyond trivial backgrounds. We show here how Hawking radiation in a collapse metric, its associated thermal spectrum, and horizon-dependence, emerges from the double copy of particle production in a background gauge field, where there is no global horizon, nor a thermal spectrum. Our approach combines worldline and amplitudes methods, and allows the unification of several classical and quantum double copy prescriptions for black hole spacetimes.

Hawking radiation from the double copy

TL;DR

The paper addresses how non-perturbative, background-dependent aspects of the gauge–gravity double copy encode black-hole physics, specifically Hawking radiation, by linking a collapsing gauge field to the Vaidya spacetime via the Kerr–Schild double copy. The authors combine worldline methods and amplitude techniques to show that mid-time particle production in a background gauge field double-copies to Hawking radiation in the gravitational collapse, with the double-copy rules (or after a shift) and connecting energy changes and eikonal phases across the collapse. They provide an exact gauge-theory calculation of the pair-creation Bogoliubov coefficients using Klein–Gordon modes expressed through Whittaker functions, and demonstrate that in the semiclassical limit these coefficients reproduce the Hawking amplitude and thermal spectrum . The result unifies several strands of double copy—classical solutions, geodesic conserved quantities, and quantum amplitudes—and suggests avenues for exploring information, backreaction, and Kerr backgrounds within the single-copy framework. Overall, the work highlights how horizon and thermal physics can be encoded in gauge-theory structures and motivates future work on late-time radiation, backreaction, and information-theoretic aspects of the double copy.

Abstract

Gravity and gauge theory are concretely linked by the double copy. Although well-studied at the level of perturbative scattering in vacuum, far less is known about non-perturbative aspects or extensions of the double copy beyond trivial backgrounds. We show here how Hawking radiation in a collapse metric, its associated thermal spectrum, and horizon-dependence, emerges from the double copy of particle production in a background gauge field, where there is no global horizon, nor a thermal spectrum. Our approach combines worldline and amplitudes methods, and allows the unification of several classical and quantum double copy prescriptions for black hole spacetimes.

Paper Structure

This paper contains 7 sections, 32 equations, 2 figures.

Table of Contents

  1. Introduction.
  2. From classical to quantum.
  3. Hawking radiation from the double copy.
  4. The exact calculation in gauge theory.
  5. Conclusions.
  6. Appendix A:
  7. Appendix B:

Figures (2)

  • Figure 1: Left: Penrose diagram for the Vaidya spacetime (\ref{['Vaidya-metric']}) in which a null shell collapses to form a black hole. The shaded region is described by the Schwarzschild metric. Asymptotic regions of early-time and Hawking radiation are illustrated. Right: the single copy $\sqrt{\mathrm{Vaidya}}$, that is, flat Minkowski space in which a Coulomb field forms at $v=0$ (shaded region). Emitted radiation is illustrated for early, late, and mid (or 'Hawking-like') times.
  • Figure 2: The exact result for the pair creation amplitude $|\alpha^{-1}\beta|$ calculated from (\ref{['eq:expact_bogol']}), in ratio to its asymptotic limit (\ref{['betaalphainverse']}), as a function of the ratio of energies $\zeta$, for three values of charge $g^2qQ$. The asymptotic limit is reached more quickly for larger values of the charge.