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arXiv 1402.6740gr-qcastro-ph.COhep-th
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具有二阶场方程II的最一般标量张量理论中的黑洞微扰：偶宇称扇区

Black hole perturbation in the most general scalar-tensor theory with second-order field equations II: the even-parity sector

Tsutomu Kobayashi, Hayato Motohashi, Teruaki Suyama

备注：
16 pages, 1 figure; matches the published version in Phys. Rev. D; typos in Eqs. (62), (29) fixed, results unchanged
发表信息：
Phys. Rev. D 89, 084042 (2014)
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摘要：

我们执行一个完整的相对论分析偶宇称线性扰动周围的静态和球对称的解决方案，在最一般的标量张量理论与二阶场方程。本文是Kobayashi { \em et al.}（2012），其中提出了奇宇称模的线性微扰分析。将Horndeski作用量推广到二阶扰动并去掉辅助变量，得到了仅用两个动力学变量表示的偶宇称扰动的二次作用量.这两种扰动可以解释为引力波和标量波。相应地，我们得到两个条件，以避免鬼和两个条件的梯度不稳定性的情况下。每对条件中只有一个产生新的稳定性判据，因为从引力波自由度的稳定性导出的条件与奇宇称扇区中的条件一致。类似地，两种模式中的一种模式的传播速度与奇奇偶校验模式的传播速度相同，而另一种模式通常与它们不同。我们的结果适用于所有具有额外单标量自由度的引力理论，如Brans-Dicke理论、$f(R)$模型和Galileon引力。

英文摘要：

We perform a fully relativistic analysis of even-parity linear perturbations around a static and spherically symmetric solution in the most general scalar-tensor theory with second-order field equations. This paper is a sequel to Kobayashi {\em et al.} (2012), in which the linear perturbation analysis for the odd-parity modes is presented. Expanding the Horndeski action to second order in perturbations and eliminating auxiliary variables, we derive the quadratic action for even-parity perturbations written solely in terms of two dynamical variables. The two perturbations can be interpreted as the gravitational and scalar waves. Correspondingly, we obtain two conditions to evade ghosts and two conditions for the absence of gradient instabilities. Only one in each pair of conditions yields a new stability criterion, as the conditions derived from the stability of the gravitational-wave degree of freedom coincide with those in the odd-parity sector. Similarly, the propagation speed of one of the two modes is the same as that for the odd-parity mode, while the other differs in general from them. Our result is applicable to all the theories of gravitation with an extra single scalar degree of freedom such as the Brans-Dicke theory, $f(R)$ models, and Galileon gravity.

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