Covariant perturbations of f ( R ) ?> black holes: the Weyl terms
Covariant perturbations of f ( R ) ?> black holes: the Weyl terms
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f ( R ) ?> 黑洞的协变扰动：Weyl 项
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发表时间：
2015
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通讯作者：
G. Pratten
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文献类型：
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作者：
G. Pratten
在本文中，我们在f(R)引力的背景下重新讨论了Schwarzschild黑洞的非球形微扰。以前的研究能够证明f(R)Schwarzschild黑洞在奇偶宇称扇区中对引力扰动的稳定性。特别是，在f(R)引力中的Regge-Wheeler(RW)方程和Zerilli方程与它们的广义相对论(GR)方程服从相同的方程。最近，1+1+2半四分体形式被用来导出一组两个波动方程：一个用于横向无迹(张量)微扰，另一个用于表征四阶引力理论的附加标量模。主变量控制张量摄动被证明是修正的RW张量，服从与GR相同的方程。然而，众所周知，在主变量的定义中存在非唯一性。本文导出了一组两个微扰变量及其伴随的波动方程，它们以协变和规范不变的方式描述引力微扰。这些变量可以与Newman-Penrose(NP)Weyl标量以及来自2+2形式主义的主变量有关。作为这项研究的副产品，我们还得到了一组有用的结果，将NP形式主义与适用于LRS-II时空的1+1+2形式主义联系起来。
In this paper we revisit non-spherical perturbations of the Schwarzschild black hole in the context of f(R) gravity. Previous studies were able to demonstrate the stability of the f(R) Schwarzschild black hole against gravitational perturbations in both the even and odd parity sectors. In particular, it was seen that the Regge–Wheeler (RW) and Zerilli equations in f(R) gravity obey the same equations as their general relativity (GR) counterparts. More recently, the 1+1+2 semi-tetrad formalism has been used to derive a set of two wave equations: one for transverse, trace-free (tensor) perturbations and one for the additional scalar modes that characterize fourth-order theories of gravitation. The master variable governing tensor perturbations was shown to be a modified RW tensor obeying the same equation as in GR. However, it is well known that there is a non-uniqueness in the definition of the master variable. In this paper we derive a set of two perturbation variables and their concomitant wave equations that describe gravitational perturbations in a covariant and gauge invariant manner. These variables can be related to the Newman–Penrose (NP) Weyl scalars as well as the master variables from the 2+2 formalism. As a byproduct of this study, we also derive a set of useful results relating the NP formalism to the 1+1+2 formalism valid for LRS-II spacetimes.