Black hole solutions in F(R) gravity with conformal anomaly

TL;DR

This paper explores black hole solutions within F(R) gravity incorporating conformal anomaly, revealing conditions for uncharged and charged solutions, their singularities, and stability across cosmic epochs.

Contribution

It provides analytical black hole solutions in F(R) gravity with conformal anomaly, analyzing their singularities and stability, which advances understanding beyond Einstein gravity.

Findings

Existence of uncharged and charged black hole solutions

Singularities at r=0 with Schwarzschild and Reissner-Nordström characteristics

Models can be stable depending on parameters and cosmic epoch

Abstract

In this paper, we consider $F(R)=R+f(R)$ theory instead of Einstein gravity with conformal anomaly and look for its analytical solutions. Depending on the free parameters, one may obtain both uncharged and charged solutions for some classes of $F(R)$ models. Calculation of Kretschmann scalar shows that there is a singularity located at $r=0$, which the geometry of uncharged (charged) solution is corresponding to the Schwarzschild (Reissner-Nordstr\"om) singularity. Further, we discuss the viability of our models in details. We show that these models can be stable depending on their parameters and in different epoches of the universe.