Kerr-Ads和KN-Ads解在f(R)引力中的解析推广

Analytical generalization of Kerr-Ads and KN-Ads solutions in f(R)gravity

本文将Carter计算旋转黑洞的方法推广到f(R)引力,并解析计算得到了Kerr-Ads和KN-Ads解.Carter认为,测试粒子在黑洞时空背景中运动的过程要求Klein-Gordon方程是可分离变量的.该物理条件会反过来约束时空度规的形式,使其成为可分离正则度规形式.基于该度规形式并假定Ricci标量为常数,本文分别计算得到了f(R)引力中的旋转不带电黑洞和旋转带电黑洞.本文的所有计算过程都是严格的解析推导.在计算Einstein张量时,我们采用了活动标架法,并利用了Cartan结构方程.为了能够快速简洁地得到解析解,我们主要求解了Einstein方程中的3个分量,并给出了这3个方程的尝试解.值得注意的是,本文没有选取特定的f(R)模型,计算是在最一般的f(R)理论中进行.该解析计算过程是普适的,能够应用于其他修正引力.

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.