We extend the standard Kerr-Schild solution generating method to higher order scalar tensor theories that are shift-invariant for the scalar field. Certain degeneracy conditions, crucial for the absence of Ostrogradski ghosts, are found to be required for the validity of the Kerr-Schild ansatz while on the other hand, theories with no parity symmetry are excluded from the solution generating method. The extended Kerr-Schild symmetry turns out to be a very useful tool to easily construct black hole solutions from simple seed configurations. In particular, the generating method developed is adapted to construct generic black holes but also regular black hole solutions within Degenerate Higher Order Scalar Tensor (DHOST) theories. As a particular example we show how to construct explicitly the Hayward metric as a solution to a specific DHOST theory.

中文翻译：

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DHOST 理论中通过 Kerr-Schild 构造的规则黑洞

我们将标准的 Kerr-Schild 解生成方法扩展到对标量场具有平移不变性的高阶标量张量理论。发现某些对不存在 Ostrogradski 鬼影至关重要的简并条件是 Kerr-Schild ansatz 有效性所必需的，而另一方面，解决方案生成方法排除了没有奇偶对称性的理论。扩展的 Kerr-Schild 对称性被证明是一个非常有用的工具，可以从简单的种子配置中轻松构建黑洞解决方案。特别是，所开发的生成方法适用于构造通用黑洞以及退化高阶标量张量 (DHOST) 理论中的规则黑洞解决方案。作为一个特定的例子，我们展示了如何明确构建海沃德度量作为特定 DHOST 理论的解决方案。