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Bejarano, C., Delhom, A., Jimenez-Cano, A., Olmo, G. J., & Rubiera-Garcia, D. (2020). Geometric inequivalence of metric and Palatini formulations of General Relativity. Phys. Lett. B, 802, 135275–4pp.
Abstract: Projective invariance is a symmetry of the Palatini version of General Relativity which is not present in the metric formulation. The fact that the Riemann tensor changes nontrivially under projective transformations implies that, unlike in the usual metric approach, in the Palatini formulation this tensor is subject to a gauge freedom, which allows some ambiguities even in its scalar contractions. In this sense, we show that for the Schwarzschild solution there exists a projective gauge in which the (affine) Kretschmann scalar, K (R beta μnu R alpha beta μnu)-R-alpha, can be set to vanish everywhere. This puts forward that the divergence of curvature scalars may, in some cases, be avoided by a gauge transformation of the connection.
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Bejarano, C., Lobo, F. S. N., Olmo, G. J., & Rubiera-Garcia, D. (2017). Palatini wormholes and energy conditions from the prism of general relativity. Eur. Phys. J. C, 77(11), 776–13pp.
Abstract: Wormholes are hypothetical shortcuts in space-time that in general relativity unavoidably violate all of the pointwise energy conditions. In this paper, we consider several wormhole spacetimes that, as opposed to the standard designer procedure frequently employed in the literature, arise directly from gravitational actions including additional terms resulting from contractions of the Ricci tensor with the metric, and which are formulated assuming independence between metric and connection (Palatini approach). We reinterpret such wormhole solutions under the prism of General Relativity and study the matter sources that thread them. We discuss the size of violation of the energy conditions in different cases and how this is related to the same spacetimes when viewed from the modified gravity side.
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Bazeia, D., Marques, M. A., & Olmo, G. J. (2018). Small and hollow magnetic monopoles. Phys. Rev. D, 98(2), 025017–8pp.
Abstract: We deal with the presence of magnetic monopoles in a non-Abelian model that generalizes the standard 't Hooft-Polyakov model in three spatial dimensions. We investigate the energy density of the static and spherically symmetric solutions to find first order differential equations that solve the equations of motion. The system is further studied and two distinct classes of solutions are obtained, one that can also be described by analytical solutions and is called a small monopole, since it is significantly smaller than the standard 't Hooft-Polyakov monopole. The other type of structure is the hollow monopole, since the energy density is endowed with a hole at its core. The hollow monopole can be smaller or larger than the standard monopole, depending on the value of the parameter that controls the magnetic permeability of the model.
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Bazeia, D., Losano, L., & Olmo, G. J. (2018). Novel connection between lump-like structures and quantum mechanics. Eur. Phys. J. Plus, 133(7), 251–10pp.
Abstract: This work deals with lump-like structures in models described by a single real scalar field in two-dimensional spacetime. We start with a model that supports lump-like configurations and use the deformation procedure to construct scalar field theories that support both lumps and kinks, with the corresponding stability investigation giving rise to new physical systems. Very interestingly, we find models that support stable topological solutions, with the stability potential being able to support a tower of non-negative bound states, generating distinct families of potentials of current interest to quantum mechanics. We also describe models where the lump-like solutions give rise to stability potentials that have the shape of a double well.
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Bazeia, D., Lobao, A. S., Losano, L., Menezes, R., & Olmo, G. J. (2015). Braneworld solutions for modified theories of gravity with nonconstant curvature. Phys. Rev. D, 91(12), 124006–11pp.
Abstract: We study braneworld models in the presence of scalar field in a five-dimensional geometry with a single extra dimension of infinite extent, with gravity modified to include a function of the Ricci scalar. We develop a procedure that allows us to obtain an analytical solution for the braneworld configuration in a diversity of models, in the much harder case where the Ricci scalar is a nonconstant quantity.
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