# Invariance of Unruh and Hawking radiation under matter-induced supertranslations

## TL;DR

This paper demonstrates that matter-induced supertranslations do not alter the fundamental Unruh and Hawking radiation spectra, although they influence scattering amplitudes and excited state observables.

## Contribution

It shows that matter-induced supertranslations leave the Unruh and Hawking radiation spectra invariant, highlighting their robustness against certain spacetime transformations.

## Key findings

- Unruh effect remains unchanged under matter-induced supertranslations
- Excited states exhibit dependence on shock wave form factors
- Supertranslations do not modify the Hawking radiation spectrum

## Abstract

Matter fields are supertranslated upon crossing a shock wave, which leads to entanglement of the quantum vacuum between the two regions on either side of the shock wave. We probe this entanglement for a scalar field in a planar shock wave background by computing the Bogoliubov transformation between the inertial and uniformly accelerated observer. The resulting Bogoliubov coefficients are shown to reproduce the standard Unruh effect without dependence on the form factor of the shock wave. In contrast, excited states lead to observables that depend upon the form factor. In the context of nonspherical gravitational collapse, we comment that the angular dependence of the limiting advanced time leads to similar supertranslation effects that do not affect the Hawking spectrum but do affect scattering amplitudes.