Analytic charged BHs in f(R) gravity

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In this article, we seek exact charged spherically symmetric black holes (BHs) with considering f(R) gravitational theory. This BH is 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 Einstein's 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 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 show the effect of the higher-order–curvature theory. Finally, we study the stability analysis using the odd-type mode and show that all the BHs are stable and have radial speed equal to one.

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