论文标题
在偏移对称的Horndeski理论中，黑洞的线性稳定性具有时间无关的标量场
Linear stability of black holes in shift-symmetric Horndeski theories with a time-independent scalar field
论文作者
论文摘要
我们研究有关静态和球形对称黑洞的线性扰动，其在移位对称Horndeski理论中具有时间独立的背景标量场，其Lagrangian的特征在于仅取决于标量场$ x $的动力学函数。我们阐明了在奇数和偶数扰动中沿着径向和角方向沿着径向和角度方向没有幽灵和拉普拉斯的不稳定性的条件。对于反射对称的理论，由k词拉格朗日和与RICCI标量的非微分衍生物耦合所描述，我们表明，与非平凡的标量头发赋予的黑洞一般不稳定。这包括当非微小衍生物耦合到RICCI标量是$ x $的线性函数时，已知存在的非矩形黑洞已知。我们还研究了非反射对称理论中的几种黑洞溶液。对于带有爱因斯坦 - 希尔伯特（Einstein-Hilbert）术语的立方体gali琴，存在一个非刺激性平坦的毛茸茸的黑洞，没有鬼魂/拉普拉斯的不稳定性。同样，对于与高斯式术语线性耦合的标量字段，相对于小耦合而构建的渐近平坦黑洞解决方案无鬼/laplacian的稳定性。
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.
