Inner Structure of Black Holes in Eddington-inspired Born-Infeld gravity: the role of mass inflation

We investigate the interior dynamics of accreting black holes in Eddington-inspired Born-Infeld gravity using the homogeneous approximation and taking charge as a surrogate for angular momentum, showing that accretion can have an enormous impact on their inner structure. We find that, unlike in general relativity, there is a minimum accretion rate bellow which the mass inflation instability, which drives the centre-of-mass streaming density to exponentially high values in an extremely short interval of time, does not occur. We further show that, above this threshold, mass inflation takes place inside black holes very much in the same way as in general relativity, but is brought to a halt at a maximum energy density which is, in general, much smaller than the fundamental energy density of the theory. We conjecture that some of these results may be a common feature of modified gravity theories in which significant deviations from general relativity manifest themselves at very high densities.