Nonsingular black holes in quadratic Palatini gravity

TL;DR

This paper demonstrates that quadratic modifications to general relativity in the Palatini formalism can produce nonsingular, charged black holes with a microscopic core, avoiding singularities at the Planck scale.

Contribution

It introduces a model where charged black holes are nonsingular due to Ricci-squared terms in Palatini gravity, providing explicit conditions for regularity.

Findings

Charged black holes can be nonsingular with a microscopic core.

The core radius scales with the square root of the charge number.

External horizons of such black holes are nearly Schwarzschild for astrophysical charges.

Abstract

We find that if general relativity is modified at the Planck scale by a Ricci-squared term, electrically charged black holes may be nonsingular. These objects concentrate their mass in a microscopic sphere of radius $r_{core}\approx N_q^{1/2}l_P/3$, where $l_P$ is the Planck length and $N_q$ is the number of electric charges. The singularity is avoided if the mass of the object satisfies the condition $M_0^2\approx m_P^2 \alpha_{em}^{3/2} N_q^3/2$, where $m_P$ is the Planck mass and $\alpha_{em}$ is the fine-structure constant. For astrophysical black holes this amount of charge is so small that their external horizon almost coincides with their Schwarzschild radius. We work within a first-order (Palatini) approach.