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

Abstract

In this article, we seek exact charged spherically symmetric black holes (BHs) with considering f (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-Nordström BH in the lower order of f (R). This means that we can not reproduce Reissner-Nordström BH in lower-order-curvature theory, i.e., in GR limit f (R) = 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.

Spherically symmetric charged black holes in f(R) gravitational theories

“…Analytic charged D-dimensional BH solutions are derived and discussed in [49]. Moreover, analytic spherically symmetric BH solutions with/without electric charge are derived in [1,50]. Those BH solutions different from the BH solutions of GR and coincide with them under certain special condition.…”

Exact Black Hole Solutions with a Conformally Coupled Scalar Field and Dynamic Ricci Curvature in $f(R)$ Gravity Theories

“…In the context of f (R) gravity (for a review see [21,22]) several black hole solutions have been found recently. Vacuum solutions were discussed in [23][24][25][26]42], while charged black hole solutions were also found in [29][30][31][32][33][34][35]38]. In [36], dynamical black holes, characterized by time-varying apparent horizons, in various theories of gravity, including the f (R) theory were investigated.…”

Black holes of $(2+1)$-dimensional $f(R)$ gravity coupled to a scalar field

“…Several black hole solutions in these theories were found and they either are deviations of the known black hole solutions of General Relativity, or they possess new properties that should be investigated. Static and spherically symmetric black hole solutions were derived in (3 + 1) and (2 + 1) dimensions [43][44][45][46], while in [47][48][49][50][51][52] charged and rotating solutions were discussed. Static and spherically symmetric black hole solutions were investigated with constant curvature, with and without electric charge and cosmological constant in [53][54][55].…”