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 \(r_{\mathrm{core}}\approx N_{q}^{1/2}l_{\mathrm{P}}/3\), 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 \(M_{0}^{2}\approx m_{\mathrm{P}}^{2} \alpha_{\mathrm{em}}^{3/2} N_{q}^{3}/2\), where m P is the Planck mass and α 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.
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Notes
In general, for Palatini f(R,Q) theories the vacuum field equations boil down to GR with an effective cosmological constant.
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Acknowledgements
This work is supported by the Spanish grant FIS2008-06078-C03-02, the Consolider Program CPAN (CSD2007-00042), and the JAE-doc program. Useful comments by A. Fabbri, J. Morales and J. Navarro-Salas are kindly acknowledged.
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Olmo, G.J., Rubiera-Garcia, D. Nonsingular black holes in quadratic Palatini gravity. Eur. Phys. J. C 72, 2098 (2012). https://doi.org/10.1140/epjc/s10052-012-2098-7
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DOI: https://doi.org/10.1140/epjc/s10052-012-2098-7