On Radiative Fluxes and Coulombic Charges in the Balance Law for Black Hole Evaporation

TL;DR

This paper examines the balance law for black hole evaporation, identifying radiative fluxes and Coulombic charges, and finds quantum corrections to the Bondi mass related to Hawking radiation entanglement entropy.

Contribution

It provides a classical and semiclassical analysis of radiative fluxes in black hole evaporation, revealing quantum corrections and clarifying flux formulas beyond standard results.

Findings

Quantum correction to Bondi mass depends on Hawking radiation entanglement entropy

Renormalized radiative flux is positive and differs from Fulling-Davies formula

Relation to 2D dilatonic black holes and implications for 3+1D evaporation

Abstract

In asymptotically-flat spacetimes, there is a clear distinction between radiative fluxes and Coulombic charges, and their relation is encoded in balance laws. In this paper, we first identify at the classical level the radiative energy flux for a minimally-coupled massless scalar field in 3+1 dimensions, and then investigate the balance law for the Bondi mass in black hole evaporation. In the usual spherically-symmetric model, the semiclassical balance law for the radiative flux implies that the Bondi mass receives a quantum correction which depends on the entanglement entropy of the Hawking radiation. Furthermore, the renormalized expectation value of the radiative flux turns out to be manifestly positive and does not coincide with the standard Fulling-Davies formula. We clarify the relation of this result to the Ashtekar-Taveras-Varadarajan proposal for 2d dilatonic black holes, and discuss its implications for black hole evaporation in 3+1 dimensions.