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arXiv 2201.09687gr-qcastro-ph.COhep-th
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与时间无关的标量场平移对称Horndeski理论中黑洞的线性稳定性

Linear stability of black holes in shift-symmetric Horndeski theories with a time-independent scalar field

Masato Minamitsuji, Kazufumi Takahashi, Shinji Tsujikawa

摘要:

在平移对称Horndeski理论中,研究了具有与时间无关的背景标量场的静态和球对称黑洞的线性微扰,其拉格朗日量的特征在于耦合函数只依赖于标量场的动力学项$X$ .我们澄清的情况下,鬼和拉普拉斯不稳定性沿径向和角度方向的奇,偶宇称扰动。对于由k-本质拉格朗日量和与Ricci标量耦合的非最小导数描述的反射对称理论,我们证明了具有非平凡标量头发的黑洞在视界附近一般是不稳定的。这包括非渐近平坦的黑洞已知存在的非最小导数耦合到里奇标量是一个线性函数的$X$。我们还研究了非反射对称理论中的几个黑洞解。对于具有Einstein-Hilbert项的立方伽利略子,存在一个非渐近平坦的多毛黑洞,没有鬼/拉普拉斯不稳定性。此外,对于线性耦合到高斯-邦纳项的标量场,渐近平坦的黑洞解相对于一个小的耦合微扰构造是免费的鬼/拉普拉斯不稳定性。

英文摘要:

We study linear perturbations about static and spherically symmetric black holes with a time-independent background scalar field in shift-symmetric Horndeski theories, whose Lagrangian is characterized by coupling functions depending only on the kinetic term of the scalar field $X$. We clarify conditions for the absence of ghosts and Laplacian instabilities along the radial and angular directions in both odd- and even-parity perturbations. For reflection-symmetric theories described by a k-essence Lagrangian and a nonminimal derivative coupling with the Ricci scalar, we show that black holes endowed with nontrivial scalar hair are unstable around the horizon in general. This includes nonasymptotically flat black holes known to exist when the nonminimal derivative coupling to the Ricci scalar is a linear function of $X$. We also investigate several black hole solutions in nonreflection-symmetric theories. For cubic Galileons with the Einstein-Hilbert term, there exists a nonasymptotically flat hairy black hole with no ghosts/Laplacian instabilities. Also, for the scalar field linearly coupled to the Gauss-Bonnet term, asymptotically flat black hole solutions constructed perturbatively with respect to a small coupling are free of ghosts/Laplacian instabilities.

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