Analytic charged BHs in $f(\mathcal{R})$ gravity

TL;DR

This paper derives exact charged black hole solutions in $f( ext{R})$ gravity, analyzing their physical, stability, and thermodynamic properties, revealing deviations from Einstein's general relativity and milder singularities.

Contribution

It presents new exact charged black hole solutions in $f( ext{R})$ gravity characterized by convolution and error functions, not reducible to Reissner-Nordström black holes in GR.

Findings

Solutions deviate from GR depending on integration constants

Black holes are stable with milder singularities

Thermodynamics influenced by higher-order curvature effects

Abstract

In this article, we seek exact charged spherically symmetric black holes (BHs) with considering $f(\mathcal{R})$ gravitational theory. These BHs are characterized by convolution and error functions. Those two functions depend on a constant of integration which is responsible to make such a solution deviate from the Einstein general relativity (GR). The error function which constitutes the charge potential of the Maxwell field depends on the constant of integration and when this constant is vanishing we can not reproduce the Reissner-Nordstr\"om BH in the lower order of $f(\mathcal{R})$. This means that we can not reproduce Reissner-Nordstr\"om BH in lower-order-curvature theory, i.e., in GR limit $f(\mathcal{R})=\mathcal{R}$, we can not get the well known charged BH. We study the physical properties of these BHs and show that it is asymptotically approached as a flat spacetime or approach AdS/dS spacetime. Also, we calculate the invariants of the BHS and show that the singularities are milder than those of BH's of GR. Additionally, we derive the stability condition through the use of geodesic deviation. Moreover, we study the thermodynamics of our BH and investigate the impact of the higher-order-curvature theory. Finally, we show that all the BHs are stable and have radial speed equal to one through the use of odd-type mode.