Super-Hawking Radiation

TL;DR

This paper explores how supertranslations and superrotations modify Hawking radiation spectra, revealing that superrotations can alter the emission spectrum and cause divergences, with implications for understanding black hole radiation and cosmic strings.

Contribution

It introduces the effects of superrotations on Hawking radiation spectra, including modifications and divergences, extending previous work on supertranslations.

Findings

Supertranslations leave the spectrum unchanged but introduce off-diagonal phases.

Superrotations modify the emission spectrum depending on the conformal factor.

Ultraviolet divergences occur in emitted power for superrotations, linked to cosmic strings.

Abstract

We discuss modifications to the Hawking spectrum that arise when the asymptotic states are supertranslated or superrotated. For supertranslations we find nontrivial off-diagonal phases in the two-point correlator although the emission spectrum is eventually left unchanged, as previously pointed out in the literature. In contrast, superrotations give rise to modifications which manifest themselves in the emission spectrum and depend nontrivially on the associated conformal factor at future null infinity. We study Lorentz boosts and a class of superrotations whose conformal factors do not depend on the azimuthal angle on the celestial sphere and whose singularities at the north and south poles have been associated to the presence of a cosmic string. In spite of such singularities, superrotations still lead to finite spectral emission rates of particles and energy which display a distinctive power-law behavior at high frequencies for each angular momentum state. The integrated particle emission rate and emitted power, on the contrary, while finite for boosts, do exhibit ultraviolet divergences for superrotations, between logarithmic and quadratic. Such divergences can be ascribed to modes with support along the cosmic string. In the logarithimic case, corresponding to a superrotation which covers the sphere twice, the total power emitted still presents the Stefan-Boltzmann form but with an effective area which diverges logarithmically in the ultraviolet.