Olmo, G. J., & Rubiera-Garcia, D. (2012). Reissner-Nordstrom black holes in extended Palatini theories. Phys. Rev. D, 86(4), 044014–15pp.
Abstract: We study static, spherically symmetric solutions with an electric field in an extension of general relativity 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-Nordstrom solution, though the structure of horizons may be different. In fact, besides the structures found in the Reissner-Nordstrom solution of general relativity, 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.
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Olmo, G. J., & Rubiera-Garcia, D. (2012). Nonsingular black holes in quadratic Palatini gravity. Eur. Phys. J. C, 72(8), 2098–5pp.
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) approximate to 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) approximate to m(P)(2)alpha N-3/2(em)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.
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Olmo, G. J., & Rubiera-Garcia, D. (2012). Nonsingular Charged Black Holes A La Palatini. Int. J. Mod. Phys. D, 21(8), 1250067–6pp.
Abstract: We argue that the quantum nature of matter and gravity should lead to a discretization of the allowed states of the matter confined in the interior of black holes. To support and illustrate this idea, we consider a quadratic extension of general relativity (GR) formulated a la Palatini and show that nonrotating, electrically charged black holes develop a compact core at the Planck density which is nonsingular if the mass spectrum satisfies a certain discreteness condition. We also find that the area of the core is proportional to the number of charges times the Planck area.
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Olmo, G. J., & Rubiera-Garcia, D. (2013). Importance of torsion and invariant volumes in Palatini theories of gravity. Phys. Rev. D, 88(8), 084030–11pp.
Abstract: We study the field equations of extensions of general relativity formulated within a metric-affine formalism setting torsion to zero (Palatini approach). We find that different (second-order) dynamical equations arise depending on whether torsion is set to zero (i) a priori or (ii) a posteriori, i.e., before or after considering variations of the action. Considering a generic family of Ricci-squared theories, we show that in both cases the connection can be decomposed as the sum of a Levi-Civita connection and terms depending on a vector field. However, while in case (i) this vector field is related to the symmetric part of the connection, in (ii) it comes from the torsion part and, therefore, it vanishes once torsion is completely removed. Moreover, the vanishing of this torsion-related vector field immediately implies the vanishing of the antisymmetric part of the Ricci tensor, which therefore plays no role in the dynamics. Related to this, we find that the Levi-Civita part of the connection is due to the existence of an invariant volume associated with an auxiliary metric h(mu v), which is algebraically related with the physical metric g(mu v).
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Olmo, G. J., & Rubiera-Garcia, D. (2014). Semiclassical geons at particle accelerators. J. Cosmol. Astropart. Phys., 02(2), 010–25pp.
Abstract: We point out that in certain four-dimensional extensions of general relativity constructed within the Palatini formalism stable self-gravitating objects with a discrete mass and charge spectrum may exist. The incorporation of nonlinearities in the electromagnetic field may effectively reduce their mass spectrum by many orders of magnitude. As a consequence, these objects could be within (or near) the reach of current particle accelerators. We provide an exactly solvable model to support this idea.
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