Importance of torsion and invariant volumes in Palatini theories of gravity

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 to an auxiliary metric $h_{\mu\nu}$, which is algebraically related with the physical metric $g_{\mu\nu}$.Comment: 14 one-column pages, no figures; v2: some minor changes and typos corrections, new references adde

Nonsingular black holes, wormholes, and de Sitter cores from anisotropic fluids

We study Born-Infeld gravity coupled to an anisotropic fluid in a static, spherically symmetric background. The free function characterizing the fluid is selected on the following grounds: i) recovery of the Reissner-Nordstr\"om solution of GR at large distances, ii) fulfillment of classical energy conditions and iii) inclusion of models of nonlinear electrodynamics as particular examples. Four branches of solutions are obtained, depending on the signs of two parameters on the gravity and matter sectors. On each branch, we discuss in detail the modifications on the innermost region of the corresponding solutions, which provides a plethora of configurations, including nonsingular black holes and naked objects, wormholes and de Sitter cores. The regular character of these configurations is discussed according to the completeness of geodesics and the behaviour of curvature scalars.Comment: 15 double column pages; 7 figure

Geometric aspects of charged black holes in Palatini theories

Charged black holes in gravity theories in the Palatini formalism present a number of unique properties. Their innermost structure is topologically nontrivial, representing a wormhole supported by a sourceless electric flux. For certain values of their effective mass and charge curvature divergences may be absent, and their event horizon may also disappear yielding a remnant. We give an overview of the mathematical derivation of these solutions and discuss their geodesic structure and other geometric properties.Comment: 6 pages. Proceedings of the conference "Spanish Relativity Meeting - ERE2014", held in Valencia (Spain

Nonsingular Black Holes in f(R)f(R) Theories

We study the structure of a family of static, spherically symmetric space-times generated by an anisotropic fluid and governed by a particular type of $f(R)$ theory. We find that for a range of parameters with physical interest, such solutions represent black holes with the central singularity replaced by a finite size wormhole. We show that time-like geodesics and null geodesics with nonzero angular momentum never reach the wormhole throat due to an infinite potential barrier. For null radial geodesics, it takes an infinite affine time to reach the wormhole. This means that the resulting space-time is geodesically complete and, therefore, nonsingular despite the generic existence of curvature divergences at the wormhole throat.Comment: Universe special issue: Open questions in black hole physic