Nonsingular Black Holes in Palatini Extensions of General Relativity

Abstract

An introduction to extended theories of gravity formulated in metric-affine (or Palatini) spaces is presented. Focusing on spherically symmetric configurations with electric fields, we will see that in these theories the central singularity present in General Relativity is generically replaced by a wormhole structure. The resulting space-time becomes geodesically complete and, therefore, can be regarded as nonsingular. We illustrate these properties considering two different models, namely, a quadratic f (R) theory and a Born-Infeld like gravity theory.

Global monopole in Palatinif(R)gravity

“…We can observe that R µ ν (h) corresponds to second order in derivatives of h µν , and the other quantities in (5) depend on matter. For a given algebraic structure of the energy-momentum tensor, the equation (5) can be solved to obtain h µν and, using h µν = f R g µν , one obtains g µν [20]. This is the approach we will follow in the next section.…”

“…As a consequence, massive particles and light rays falling into the black hole have incomplete paths because their corresponding affine parameters cannot be extended beyond the center. Following the approach presented in [20], we will now explore if the space-times resulting from our model are geodesically complete or not. Before going into the details, it is useful to make some observations, since we are working with the coordinate x instead of the radial function r(x).…”

“…From this perspective, we will discuss the novelties that alternative theories of gravity can bring to the question of the black hole with the GM load in Palatini formalism. Our motivation stems from the work [20] in which the author discussed black hole solutions in this formalism in spherically symmetric, static configurations which turn out to be geodesically complete. As we will see, some of our solutions also share this feature.…”

Multicenter solutions in Eddington-inspired Born–Infeld gravity

“…For spherically symmetric spacetimes the geodesic equation can be written in a simple form [53], which for the line element (40) becomes…”

Palatini wormholes and energy conditions from the prism of general relativity

“…It has been recently established [96] that Palatini theories in which the gravity Lagrangian is a function of the Ricci tensor and the metric, , lead to field equations of the formwhere represents the determinant of a matrix which relates the physical metric and an auxiliary metric which is compatible with the affine connection that defines the Ricci tensor. In other words, and .…”