标题： 球对称、静态的带有标量场的黑洞以及非最小耦合k-本质中的裸奇点 显示英文标题

标题： Spherically symmetric, static black holes with scalar hair, and naked singularities in nonminimally coupled k-essence

摘要： 我们应用了一种最近发展的时空2+1+1分解，基于非正交双叶层结构，用于研究Horndeski标量-张量理论中的球对称静态黑洞解。 我们的讨论采用修改引力的有效场论（EFT）方法，其中作用量依赖于适应非正交2+1+1分解的度规和嵌入标量。 我们证明了与观测相容的最一般的Horndeski拉格朗日量可以表示为这种EFT形式。 通过研究EFT作用量的一阶扰动，我们导出了三个运动方程，这些方程在正交2+1+1分解中之前已导出，还有一个关于与叶层非正交性相关的度规参数N的第四方程。 对于具有零$G_3$和$G_5$但一般函数$G_2(\phi,X)$（k-本质）和$G_4(\phi)$（与度规的非最小耦合）的Horndeski理论类，我们证明了唯一性定理，即除了爱因斯坦-希尔伯特作用量外，没有其他作用量允许施瓦茨希尔德解。 接下来，我们求解仅有一个独立度规函数的情况下的EFT场方程，得到了由一个被解释为质量或潮汐电荷、宇宙学常数和第三个参数表征的新解。 这些解代表裸奇点、带有标量头发的黑洞，或者具有施瓦茨希尔德-德西特时空的双视界结构。 还出现了具有均匀Kantowski-Sachs类型区域的解。 最后，对于在曲率坐标中线性函数$G_4$，在某些参数范围内，其中一个解表现出一种有趣的对数奇点，位于视界之外。 新推导出的带标量头发的黑洞解通过渐近非平坦性避开了以前已知的唯一性定理，即使在没有宇宙学常数的情况下也是如此。 显示英文摘要

摘要： We apply a recently developed 2+1+1 decomposition of spacetime, based on a nonorthogonal double foliation for the study of spherically symmetric, static black hole solutions of Horndeski scalar-tensor theory. Our discussion proceeds in an effective field theory (EFT) of modified gravity approach, with the action depending on metric and embedding scalars adapted to the nonorthogonal 2+1+1 decomposition. We prove that the most generic class of Horndeski Lagrangians compatible with observations can be expressed in this EFT form. By studying the first order perturbation of the EFT action we derive three equations of motion, which reduce to those derived earlier in an orthogonal 2+1+1 decomposition, and a fourth equation for the metric parameter N related to the nonorthogonality of the foliation. For the Horndeski class of theories with vanishing $G_3$ and $G_5$, but generic functions $G_2(\phi,X)$ (k-essence) and $G_4(\phi)$ (nonminimal coupling to the metric) we prove the unicity theorem that no action beyond Einstein--Hilbert allows for the Schwarzschild solution. Next we integrate the EFT field equations for the case with only one independent metric function obtaining new solutions characterized by a parameter interpreted as either mass or tidal charge, the cosmological constant and a third parameter. These solutions represent naked singularities, black holes with scalar hair or have the double horizon structure of the Schwarzschild--de Sitter spacetime. Solutions with homogeneous Kantowski--Sachs type regions also emerge. Finally, one of the solutions obtained for the function $G_4$ linear in the curvature coordinate, in certain parameter range exhibits an intriguing logarithmic singularity lying outside the horizon. The newly derived hairy black hole solutions evade previously known unicity theorems by being asymptotically nonflat, even in the absence of the cosmological constant.