Stealth Schwarzschild solution in shift symmetry breaking theories
Stealth Schwarzschild solution in shift symmetry breaking theories
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DOI：
10.1103/physrevd.98.084027
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发表时间：
2018-09
影响因子：
5
通讯作者：
Masato Minamitsuji;H. Motohashi
中科院分区：
文献类型：
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作者：
Masato Minamitsuji;H. Motohashi
我们发现隐形史瓦西解决方案的标量场的非平凡的配置文件在爱因斯坦引力耦合到标量场的k-本质和/或广义立方伽利略条款，这是一个子类的Horndeski理论打破了移位对称性，其中的引力波的传播速度与光速相一致的地平线上的规则。在推导出移位对称破缺理论允许具有非平凡标量场轮廓的一般Ricci平坦度规解的充分条件后，我们重点讨论了具有或不具有时间依赖性的标量场的隐形Schwarzschild解。对于剖面$\phi=\phi_0（r）$，我们得到了两种隐形Schwarzschild解，其中一种在视界上是正则的.线性微扰分析表明，标量模的动力学项完全消失，表明标量模是强耦合的。在一般标量场分布只依赖于空间坐标的理论中，对于隐形史瓦西解，不可避免地会出现二次作用量中标量模动力学项的缺失。另一方面，对于含时标量场分布，我们澄清了在位移对称破缺理论中不存在隐形史瓦西解。
We find stealth Schwarzschild solutions with a nontrivial profile of the scalar field regular on the horizon in the Einstein gravity coupled to the scalar field with the k-essence and/or generalized cubic galileon terms, which is a subclass of the Horndeski theory breaking the shift symmetry, where the propagation speed of gravitational waves coincides with the speed of light. After deriving sufficient conditions for the shift symmetry breaking theory to allow a general Ricci-flat metric solution with a nontrivial scalar field profile, we focus on the stealth Schwarzschild solution with the scalar field with or without time dependence. For the profile $\phi=\phi_0(r)$, we explicitly obtain two types of stealth Schwarzschild solutions, one of which is regular on the event horizon. The linear perturbation analysis clarifies that the kinetic term of the scalar mode identically vanishes, indicating that the scalar mode is strongly coupled. The absence of the kinetic term of the scalar mode in the quadratic action would inevitably arise for the stealth Schwarzschild solutions in the theory with a general scalar field profile depending only on the spatial coordinates. On the other hand, for the time-dependent scalar field profile, we clarify that there does not exist a stealth Schwarzschild solution in the shift symmetry breaking theories.