Bazeia, D., Losano, L., Menezes, R., Olmo, G. J., & Rubiera-Garcia, D. (2015). Thick brane in f(R) gravity with Palatini dynamics. Eur. Phys. J. C, 75, 569–10pp.
Abstract: This work deals with modified gravity in five dimensional spacetime. We study a thick Palatini f(R) brane, that is, a braneworld scenario described by an anti-de Sitter warped geometry with a single extra dimension of infinite extent, sourced by real scalar field under the Palatini approach, where the metric and the connection are regarded as independent degrees of freedom. We consider a first-order framework which we use to provide exact solutions for the scalar field and warp factor. We also investigate a perturbative scenario such that the Palatini approach is implemented through a Lagrangian f(R)=R+ϵR^n, where the small parameter ϵ controls the deviation from the standard thick brane case.
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Olmo, G. J., & Rubiera-Garcia, D. (2011). Palatini f(R) black holes in nonlinear electrodynamics. Phys. Rev. D, 84(12), 124059–14pp.
Abstract: The electrically charged Born-Infeld black holes in the Palatini formalism for f(R) theories are analyzed. Specifically we study those supported by a theory f(R) = R +/- R(2)/R(P), where R(P) is Planck's curvature. These black holes only differ from their General Relativity counterparts very close to the center but may give rise to different geometrical structures in terms of inner horizons. The nature and strength of the central singularities are also significantly affected. In particular, for the model f(R) = R – R(2)/R(P) the singularity is shifted to a finite radius, r(+), and the Kretschmann scalar diverges only as 1/(r-r(+))(2).
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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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