Not Quite Killing It: Black Hole Evaporation, Global Energy, and De-Idealization

TL;DR

This paper critically examines the reliance on idealized symmetries like Killing vector fields in arguments for black hole evaporation, highlighting challenges in extending these conservation laws to realistic, non-idealized black hole spacetimes.

Contribution

It analyzes the limitations of using 'approximately Killing' fields to justify black hole evaporation in non-idealized, dynamic spacetimes, questioning the validity of such idealizations.

Findings

Challenges in extending conservation laws to realistic black holes

Limitations of 'approximately Killing' fields in non-stationary spacetimes

Questions raised about the justification of black hole evaporation arguments

Abstract

A family of arguments for black hole evaporation relies on conservation laws, defined through symmetries represented by Killing vector fields which exist globally or asymptotically. However, these symmetries often rely on the idealizations of stationarity and asymptotic flatness, respectively. In non-stationary or non-asymptotically-flat spacetimes where realistic black holes evaporate, the requisite Killing fields typically do not exist. Can we 'de-idealize' these idealizations, and subsequently the associated arguments for black hole evaporation? Here, I critically examine the strategy of using 'approximately Killing' fields to de-idealize black hole spacetimes and approximately extend conservation laws to non-idealized cases. I argue that this approach encounters significant challenges, undermining the use of these idealizations to justify the evaporation of realistic -- rather than idealized -- black holes, and raising questions about the justified use of such idealizations.