Energy decomposition within Einstein-Born-Infeld black holes

TL;DR

This paper explores the energy structure and horizon properties of Einstein-Born-Infeld black holes, revealing how their characteristics depend on the parameters $b$ and $Q$, and discusses implications for black hole radiation and potential observational differences.

Contribution

It generalizes the black hole mass decomposition to Einstein-Born-Infeld black holes, analyzing how their horizon structure and thermodynamics depend on the parameters $b$ and $Q$, and suggests observational signatures.

Findings

Black holes with $b|Q| extless 1/2$ can have zero irreducible mass and a single horizon.

Black holes with $b|Q| extgreater 1/2$ have a minimum irreducible mass and two horizons up to a transitional point.

Black holes with $b|Q| extgreater 1/2$ take infinite time to reach zero temperature, settling at minimum energy.

Abstract

We analyze the consequences of the recently found generalization of the Christodoulou-Ruffini black hole mass decomposition for Einstein-Born-Infeld black holes [characterized by the parameters $(Q,M,b)$, where $M = M(M_{irr},Q,b)$, $b$ scale field, $Q$ charge, $M_{irr}$ "irreducible mass", physically meaning the energy of a black hole when its charge is null] and their interactions. We show in this context that their description is largely simplified and can basically be split into two families depending upon the parameter $b|Q|$. If $b|Q|\leq 1/2$, then black holes could have even zero irreducible masses and they always exhibit single, non degenerated, horizons. If $b|Q|>1/2$, then an associated black hole must have a minimum irreducible mass (related to its minimum energy) and has two horizons up to a transitional irreducible mass. For larger irreducible masses, single horizon structures raise again. By assuming that black holes emit thermal uncharged scalar particles, we further show in light of the black hole mass decomposition that one satisfying $b|Q|>1/2$ takes an infinite amount of time to reach the zero temperature, settling down exactly at its minimum energy. Finally, we argue that depending on the fundamental parameter $b$, the radiation (electromagnetic and gravitational) coming from Einstein-Born-Infeld black holes could differ significantly from Einstein-Maxwell ones. Hence, it could be used to assess such a parameter.