Reissner-Nordstr\"om black holes in extended Palatini theories

TL;DR

This paper explores modified gravity theories in Palatini formalism, revealing new black hole solutions with nonsingular cores and different horizon structures, which could impact our understanding of black hole physics.

Contribution

It introduces static, spherically symmetric solutions with electric fields in extended Palatini gravity, showing the existence of nonsingular black holes with Planck-scale cores.

Findings

Nonsingular black holes with cores proportional to Planck area

Solutions include Schwarzschild-like horizons and naked cores

Core matter density is independent of charge and mass

Abstract

We study static, spherically symmetric solutions with an electric field in an extension of general relativity (GR) containing a Ricci-squared term and formulated in the Palatini formalism. We find that all the solutions present a central core whose area is proportional to the Planck area times the number of charges. Far from the core, curvature invariants quickly tend to those of the usual Reissner-Nordstr\"om solution, though the structure of horizons may be different. In fact, besides the structures found in the Reissner-Nordstr\"om solution of GR, we find black hole solutions with just one nondegenerate horizon (Schwarzschild-like), and nonsingular black holes and naked cores. The charge-to-mass ratio of the nonsingular solutions implies that the core matter density is independent of the specific amounts of charge and mass and of order the Planck density. We discuss the physical implications of these results for astrophysical and microscopic black holes, construct the Penrose diagrams of some illustrative cases, and show that the maximal analytical extension of the nonsingular solutions implies a bounce of the radial coordinate.