Bazeia, D., Losano, L., Olmo, G. J., & Rubiera-Garcia, D. (2014). Black holes in five-dimensional Palatini f(R) gravity and implications for the AdS/CFT correspondence. Phys. Rev. D, 90(4), 044011–8pp.
Abstract: We show that theories having second-order field equations in the context of higher-dimensional modified gravity are not restricted to the family of Lovelock Lagrangians, but can also be obtained if no a priori assumption on the relation between the metric and affine structures of space-time is made (the Palatini approach). We illustrate this fact by considering the case of Palatini f(R) gravities in five dimensions. Our results provide an alternative avenue to explore new domains of the AdS/CFT correspondence without resorting to ad hoc quasitopological constructions.
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Odintsov, S. D., Olmo, G. J., & Rubiera-Garcia, D. (2014). Born-Infeld gravity and its functional extensions. Phys. Rev. D, 90(4), 044003–8pp.
Abstract: We investigate the dynamics of a family of functional extensions of the (Eddington-inspired) Born-Infeld gravity theory, constructed with the inverse of the metric and the Ricci tensor. We provide a generic formal solution for the connection and an Einstein-like representation for the metric field equations of this family of theories. For particular cases we consider applications to the early-time cosmology and find that nonsingular universes with a cosmic bounce are very generic and robust solutions.
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Olmo, G. J., Rubiera-Garcia, D., & Sanchez-Puente, A. (2015). Geodesic completeness in a wormhole spacetime with horizons. Phys. Rev. D, 92(4), 044047–16pp.
Abstract: The geometry of a spacetime containing a wormhole generated by a spherically symmetric electric field is investigated in detail. These solutions arise in high-energy extensions of general relativity formulated within the Palatini approach and coupled to Maxwell electrodynamics. Even though curvature divergences generically arise at the wormhole throat, we find that these spacetimes are geodesically complete. This provides an explicit example where curvature divergences do not imply spacetime singularities.
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Bazeia, D., Losano, L., Olmo, G. J., Rubiera-Garcia, D., & Sanchez-Puente, A. (2015). Classical resolution of black hole singularities in arbitrary dimension. Phys. Rev. D, 92(4), 044018–15pp.
Abstract: A metric-affine approach is employed to study higher-dimensional modified gravity theories involving different powers and contractions of the Ricci tensor. It is shown that the field equations are always second-order, as opposed to the standard metric approach, where this is only achieved for Lagrangians of the Lovelock type. We point out that this property might have relevant implications for the AdS/CFT correspondence in black hole scenarios. We illustrate these aspects by considering the case of Born-Infeld gravity in d dimensions, where we work out exact solutions for electrovacuum configurations. Our results put forward that black hole singularities in arbitrary dimensions can be cured in a purely classical geometric scenario governed by second-order field equations.
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Bazeia, D., Losano, L., Olmo, G. J., & Rubiera-Garcia, D. (2017). Geodesically complete BTZ-type solutions of 2+1 Born-Infeld gravity. Class. Quantum Gravity, 34(4), 045006–21pp.
Abstract: We study Born-Infeld gravity coupled to a static, non-rotating electric field in 2 + 1 dimensions and find exact analytical solutions. Two families of such solutions represent geodesically complete, and hence nonsingular, spacetimes. Another family represents a point-like charge with a singularity at the center. Despite the absence of rotation, these solutions resemble the charged, rotating BTZ solution of general relativity but with a richer structure in terms of horizons. The nonsingular character of the first two families turn out to be attached to the emergence of a wormhole structure on their innermost region. This seems to be a generic prediction of extensions of general relativity formulated in metric-affine (or Palatini) spaces, where metric and connection are regarded as independent degrees of freedom.
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