Afonso, V. I., Olmo, G. J., & Rubiera-Garcia, D. (2018). Mapping Ricci-based theories of gravity Into general relativity. Phys. Rev. D, 97(2), 021503–6pp.
Abstract: We show that the space of solutions of a wide class of Ricci-based metric-affine theories of gravity can be put into correspondence with the space of solutions of general relativity (GR). This allows us to use well-established methods and results from GR to explore new gravitational physics beyond it.
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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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Afonso, V. I., Bejarano, C., Ferraro, R., & Olmo, G. J. (2022). Determinantal Born-Infeld coupling of gravity and electromagnetism. Phys. Rev. D, 105(8), 084067–11pp.
Abstract: We study a Born-Infeld inspired model of gravity and electromagnetism in which both types of fields are treated on an equal footing via a determinantal approach in a metric-aft me formulation. Though this formulation is a priori in conflict with the postulates of metric theories of gravity, we find that the resulting equations can also be obtained from an action combining the Einstein-Hilbert action with a minimally coupled nonlinear electrodynamics. As an example, the dynamics is solved for the charged static black hole.
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Beltran Jimenez, J., Heisenberg, L., & Olmo, G. J. (2015). Tensor perturbations in a general class of Palatini theories. J. Cosmol. Astropart. Phys., 06(6), 026–16pp.
Abstract: We study a general class of gravitational theories formulated in the Palatini approach and derive the equations governing the evolution of tensor perturbations. In the absence of torsion, the connection can be solved as the Christoffel symbols of an auxiliary metric which is non-trivially related to the space-time metric. We then consider background solutions corresponding to a perfect fluid and show that the tensor perturbations equations (including anisotropic stresses) for the auxiliary metric around such a background take an Einstein-like form. This facilitates the study in a homogeneous and isotropic cosmological scenario where we explicitly establish the relation between the auxiliary metric and the spacetime metric tensor perturbations. As a general result, we show that both tensor perturbations coincide in the absence of anisotropic stresses.
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Alfonso, V. I., Bejarano, C., Beltran Jimenez, J., Olmo, G. J., & Orazi, E. (2017). The trivial role of torsion in projective invariant theories of gravity with non-minimally coupled matter fields. Class. Quantum Gravity, 34(23), 235003–20pp.
Abstract: We study a large family of metric-affine theories with a projective symmetry, including non-minimally coupled matter fields which respect this invariance. The symmetry is straightforwardly realised by imposing that the connection only enters through the symmetric part of the Ricci tensor, even in the matter sector. We leave the connection completely free (including torsion), and obtain its general solution as the Levi-Civita connection of an auxiliary metric, showing that the torsion only appears as a projective mode. This result justifies the widely used condition of setting vanishing torsion in these theories as a simple gauge choice. We apply our results to some particular cases considered in the literature, including the so-called Eddington-inspired-Born-Infeld theories among others. We finally discuss the possibility of imposing a gauge fixing where the connection is metric compatible, and comment on the genuine character of the non-metricity in theories where the two metrics are not conformally related.
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