A method is presented to construct a particular, non-minimally coupled scalar–tensor theory such that a given metric is an exact vacuum solution in that theory. In contrast to the standard approach in studies of gravitational dynamics, where one begins with an action and then solves the equations of motion, this approach allows for an explicit theory to be built around some pre-specified geometry. Starting from a parameterized black hole spacetime with generic, non-Kerr hairs, it is shown how an overarching family of theories can be designed to fit the metric exactly.

中文翻译：

---

引力逆问题的一系列解决方案：围绕度量建立理论

提出了一种方法来构建一个特定的、非最小耦合的标量-张量理论，使得给定的度量是该理论中的精确真空解。与引力动力学研究中的标准方法（从一个动作开始，然后求解运动方程）相比，这种方法允许围绕某些预先指定的几何结构建立明确的理论。从具有通用非克尔毛的参数化黑洞时空开始，展示了如何设计一个总体理论系列以精确拟合度量。