f(R)引力是一个直接拓展广义相对论的修正引力理论,它的拉格朗日量是一个仅含曲率标量R 的任意函数f(R). 在F(r) = 1 + αr 的条件下(F(r)≡(df(R(r)))/(dr) 和αr 是一个对广义相对论小的修正量),导出了度规f(R)引力理论中场方程的精确球对称真空解. 此外,考虑了这个黑洞背景时空中的标量场扰动. 用六阶WKB(Wentzel-Kramers-Brillouin)方法,讨论了拟正则模和这个黑洞的参数之间的关系,得出这个黑洞是稳定的结论.%f(R)gravity is a straight extension of general relativity,in which the Lagrangian is an arbitrary function of the curvature scalar R. We derive an exact spherically symmetric vacuum solution to the field equations of the metric f (R )gravity with the condition F (r )= 1 + αr (F(r)≡(df(R(r)))/(dr)and the term αr indicates a minor correction (to general relativity). Moreover, we consider the scalar perturbations on this black hole background spacetimes. Using the six-order WKB (Wentzel-Kramers-Brillouin)method,we discuss the relations between quasinormal modes of this black hole and its parameters which show that the black hole is stable.
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