Nonrotating and rotating black hole solutions in f(R) = R − 2αR model

Abstract

In this paper, we present a detailed study of both nonrotating and rotating black hole solutions in [Formula: see text] model. The complicated expression of Ricci scalar, which appears in the vacuum field equations, brings the main difficulty of searching analytic solutions. In the case of searching nonrotating black hole solution, we use the 00 component minus 11 component of field equations to constrain the Ricci scalar. In order to obtain analytic solutions of rotating black hole, two strategies are used. One is the simplification of the line element using Carter’s consideration that the Klein–Gordon equation is separable. The other is that we give the general solutions of the simultaneous equations of 00 minus 11 component equation and 01 component of the field equations. These strategies greatly simplify the process and difficulty of solving the axisymmetric solutions. The calculation process is more friendly to generalize to other modified gravities.