Nonsingular black holes in quadratic Palatini gravity

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.

5 pages, 1 figure, revtex4-1 class; revised version, title changed, minor changes in text, equations and references

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• Reissner-Nordström black holes in extended Palatini theories
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