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.
References
S. Chandrasekhar, The density of white dwarf stars. Philos. Mag. 11, 592 (1931)
S. Chandrasekhar, The maximum mass of ideal white dwarfs. Astrophys. J. 74, 81 (1931)
S.W. Hawking, Particle creation by black holes. Commun. Math. Phys. 43, 199 (1975)
A. Fabbri, J. Navarro-Salas, Modeling Black Hole Evaporation (Imp. Coll. Press, London, 2005)
S.L. Shapiro, S.A. Teukolsky, Black Holes, White Dwarfs, and Neutron Stars (Wiley-Interscience, New York, 1983)
G.J. Olmo, Palatini approach to modified gravity: f(R) theories and beyond. Int. J. Mod. Phys. D 20, 413 (2011)
G.J. Olmo, Palatini actions and quantum gravity phenomenology. J. Cosmol. Astropart. Phys. 1110, 018 (2011)
G.J. Olmo, P. Singh, Effective action for loop quantum cosmology a la Palatini. J. Cosmol. Astropart. Phys. 0901, 030 (2009)
C. Barragan, G.J. Olmo, Isotropic and anisotropic bouncing cosmologies in Palatini gravity. Phys. Rev. D 82, 084015 (2010)
C. Barragan, G.J. Olmo, H. Sanchis-Alepuz, Bouncing cosmologies in Palatini f(R) gravity. Phys. Rev. D 80, 024016 (2009)
G.J. Olmo, H. Sanchis-Alepuz, S. Tripathi, Dynamical aspects of generalized Palatini theories of gravity. Phys. Rev. D 80, 024013 (2009)
M. Borunda, B. Janssen, M. Bastero-Gil, Palatini versus metric formulation in higher curvature gravity. J. Cosmol. Astropart. Phys. 0811, 008 (2008)
R. Blumenhagen, A. Deser, E. Plauschinn, F. Rennecke, Palatini–Lovelock–Cartan gravity—Bianchi identities for stringy fluxes. arXiv:1202.4934 [hep-th]
G.J. Olmo, D. Rubiera-Garcia, Reissner–Nordström black holes in extended Palatini theories. Phys. Rev. D (2012, to appear)
G.W. Gibbons, D.A. Rasheed, Electric–magnetic duality rotations in nonlinear electrodynamics. Nucl. Phys. B 454, 185 (1995)
T. Ortin, Gravity and Strings. Cambridge Monographs on Mathematical Physics (C.U.P., Cambridge, 2004)
G. Dvali, C. Gomez, S. Mukhanov, Probing quantum geometry at LHC. J. High Energy Phys. 1102, 012 (2011)
G. Dvali, C. Gomez, S. Mukhanov, Black hole masses are quantized. arXiv:1106.5894 [hep-ph]
S. Dimopoulos, G. Landsberg, Black holes at the LHC. Phys. Rev. Lett. 87, 161602 (2001)
S.B. Giddings, S. D Thomas, High-energy colliders as black hole factories: the end of short distance physics. Phys. Rev. D 65, 056010 (2002)
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