Hawking-like radiation from evolving black holes and compact horizonless objects

TL;DR

This paper demonstrates that Hawking-like radiation can occur in evolving black holes and horizonless objects under certain conditions, extending the understanding of black hole radiation beyond static, eternal horizons.

Contribution

It provides a quantitative analysis of Hawking-like radiation in dynamic scenarios, including evaporating black holes and horizonless collapsing objects, using time-dependent Bogoliubov coefficients.

Findings

Hawking-like radiation occurs under approximate exponential relations between null generators.

A Planck-distributed flux is produced in non-static, evolving black hole scenarios.

Explicit calculations of Bogoliubov coefficients confirm the radiation process.

Abstract

Usually, Hawking radiation is derived assuming (i) that a future eternal event horizon forms, and (ii) that the subsequent exterior geometry is static. However, one may be interested in either considering quasi-black holes (objects in an ever-lasting state of approach to horizon formation, but never quite forming one), where (i) fails, or, following the evolution of a black hole during evaporation, where (ii) fails. We shall verify that as long as one has an approximately exponential relation between the affine parameters on the null generators of past and future null infinity, then subject to a suitable adiabatic condition being satisfied, a Planck-distributed flux of Hawking-like radiation will occur. This happens both for the case of an evaporating black hole, as well as for the more dramatic case of a collapsing object for which no horizon has yet formed (or even will ever form). In this article we shall cast the previous statement in a more precise and quantitative form, and subsequently provide several explicit calculations to show how the time-dependent Bogoliubov coefficients can be calculated.