In 1981 Wyman classified the solutions of the Einstein–Klein–Gordon equations with static spherically symmetric spacetime metric and vanishing scalar potential. For one of these classes, the scalar field linearly grows with time. We generalize this symmetry noninheriting solution, perturbatively, to a rotating one and extend the static solution exactly to arbitrary spacetime dimensions. Furthermore, we investigate the existence of nonminimally coupled, time-dependent real scalar fields on top of static black holes, and prove a no-hair theorem for stealth scalar fields on the Schwarzschild background.

中文翻译：

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具有时间相关实标量场的平稳时空

1981 年，Wyman 将爱因斯坦-克莱因-戈登方程的解分类为静态球对称时空度量和消失标量势。对于其中一类，标量场随时间线性增长。我们将这种对称性非继承解微扰地推广到旋转解，并将静态解精确地扩展到任意时空维度。此外，我们研究了静态黑洞顶部非最小耦合、时间相关的实标量场的存在，并证明了 Schwarzschild 背景上隐形标量场的无毛定理。