Shift-symmetric Horndeski theories admit an interesting class of Schwarzschild black hole solutions exhibiting time-dependent scalar hair. By making use of Lemaitre coordinates, we analyze perturbations around these types of black holes, and demonstrate that scalar perturbations around black hole backgrounds inevitably have gradient instabilities. Taken together with previously established results, this newly-discovered instability rules out black holes with time-dependent scalar hair in Horndeski theories.

中文翻译：

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移对称霍恩德斯基理论中毛状黑洞的存在和不稳定性

位移对称 Horndeski 理论承认一类有趣的 Schwarzschild 黑洞解决方案展示了与时间相关的标量头发。通过利用勒梅特坐标，我们分析了这些类型黑洞周围的扰动，并证明了黑洞背景周围的标量扰动不可避免地具有梯度不稳定性。结合先前确定的结果，这种新发现的不稳定性排除了 Horndeski 理论中具有时间相关标量头发的黑洞。