Energy decomposition within Einstein-Born-Infeld black holes

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.