Analytical generalization of Kerr-Ads and KN-Ads solutions in f(R)gravity
In this study,we extend Carter's method for giving rotating black holes by applying it to f(R)gravity,successfully deriving the Kerr-Ads and KN-Ads solutions analytically.Carter highlighted that for test particles moving in the vicinity of black holes,the Klein-Gordon equation must allow for variable separation.This requirement,in turn,imposes constraints on the metric form,necessitating a separate canonical form.Using this special metric form and assuming a constant Ricci scalar,we calculate rotating uncharged and charged black holes within f(R)gravity.Our approach throughout this paper is rooted in strictly analytical derivations.To compute the Einstein tensor,we employ the moving frame method alongside Cartan's structure equation.Our focus is primarily on deriving analytical solutions quickly and succinctly,concentrating on the three components of the Einstein equations and presenting preliminary solutions.We do not commit to any specific f(R)model in this paper;instead,our calculations remain as general as possible within the f(R)theory.This analytical calculation process is universal and can be applied to other modified gravity theories.
万方数据
