Mass inflation in Eddington-inspired Born-Infeld black holes: analytical scaling solutions

TL;DR

This paper investigates the inner dynamics of accreting Eddington-inspired Born-Infeld black holes, deriving analytical conditions for mass inflation and scaling solutions, revealing a minimum accretion rate needed for inflation to occur.

Contribution

It provides the first analytical expression for the threshold accretion rate for mass inflation in Eddington-inspired Born-Infeld black holes and derives scaling solutions validated by numerical comparisons.

Findings

Mass inflation occurs only above a critical accretion rate.

Analytical scaling solutions accurately describe mass inflation dynamics.

Mass inflation ends abruptly due to rapid density variations.

Abstract

We study the inner dynamics of accreting Eddington-inspired Born-Infeld black holes using the homogeneous approximation and taking charge as a surrogate for angular momentum. We show that there is a minimum of the accretion rate below which mass inflation does not occur, and we derive an analytical expression for this threshold as a function of the fundamental scale of the theory, the accretion rate, the mass, and the charge of the black hole. Our result explicitly demonstrates that, no matter how close Eddington-inspired Born-Infeld gravity is to general relativity, there is always a minimum accretion rate below which there is no mass inflation. For larger accretion rates, mass inflation takes place inside the black hole as in general relativity until the extremely rapid density variations bring it to an abrupt end. We derive analytical scaling solutions for the value of the energy density and of the Misner-Sharp mass attained at the end of mass inflation as a function of fundamental scale of the theory, the accretion rate, the mass, and the charge of the black hole, and compare these with the corresponding numerical solutions. We find that, except for unreasonably high accretion rates, our analytical results appear to provide an accurate description of homogeneous mass inflation inside accreting Eddington-inspired Born-Infeld black holes.