A special class of solutions in F(R)-gravity

Abstract

We consider a special class of vacuum F(R)modified gravity models. The form of their Lagrangian is such that the field equations are trivially satisfied when the Ricci scalar is constant. There are many interesting F(R)models for inflation and dark energy that fall in this class. However, little is known outside the domain of cosmology therefore we aim to explore the class of solutions that are static and spherically symmetric. After some general considerations, we investigate in more detail black hole solutions, traversable wormhole metrics and, finally, configurations that can match the anomalous rotation curves of galaxies.

Thermal stability of a special class of black hole solutions in F(R) gravity

“…In this paper, we follow the method of Ref. [63], which is a special class of F(R)-gravity models with two constraints, simultaneously, F(R 0 ) = 0 and F R = 0. Taking into account the mentioned constraints, one can find that the vacuum equation (3) are automatically satisfied with arbitrary R 0 .…”

“…Consequently, our strategy is working on some viable models of F(R)-gravity that satisfy these conditions and solving the equation of constant Ricci scalar. As it is mentioned in [63], there are several models for the early-time inflation or late-time accelerated expansion that can satisfy the mentioned constraints. As a result, we regard a spherically symmetric and static solutions with constant Ricci scalar which are reported in [63] to investigate their possible phase transition.…”

“…Here, our main motivation is the study of thermodynamical and geometrical aspects of topological black hole solutions with Lifshitz-like spacetime. Therefore, we consider the metric of 4-dimensional spacetime as [63]…”

“…Hereafter, we indicate ω k as the volume of boundary t = cte and r = cte of the metric. Since we desire to study the Lifshitzlike solutions [63], we define α(r ) as…”

On the equivalence of Jordan and Einstein frames in scale-invariant gravity

“…The only exceptions are f (R) = R 2 , for which V is constant, and f (R) = R for which V = 0 and the theory is equivalent to GR. There are several examples of f (R) theories that feature spherically symmetric solutions, and such that f ′ (0) = f (0) = 0, see [18]. Typically, these models do not have a GR limit in the low curvature regime, namely lim R→0 f (R) = R so the potential (22) does not vanish in this limit and Ricci flat solutions in the EF are not allowed.…”