Static and spherically symmetric black holes in $f(R)$ theories

TL;DR

This paper investigates static, spherically symmetric black hole solutions in $f(R)$ gravity theories, deriving conditions for their existence, analyzing the effective potential near the horizon, and calculating particle collision energies.

Contribution

It provides a necessary condition for such black hole solutions in $f(R)$ theories and explores the limits on curvature at the horizon.

Findings

Existence of a limit on the curvature at the horizon.

Derived a necessary condition for static, spherically symmetric solutions.

Calculated the energy of particle collisions near the horizon.

Abstract

We study some features of static and spherically symmetric solutions (SSS) with a horizon in $f(R)$ theories of gravitation by means of a near-horizon analysis. A necessary condition for an $f(R)$ theory to have this type of solution is obtained. General features of the effective potential are deduced, and it is shown that there exists a limit on the curvature at the horizon, in both cases for any $f(R$). Finally, we calculate the expression for the energy of the collision of two masive particles in the center of mass frame.