Recently, in [1], it was demonstrated that various regular black hole metrics can be derived within a theory featuring an infinite number of higher curvature corrections to General Relativity. Moreover, truncating this infinite series at the first few orders already yields a reliable approximation of the observable characteristics of such black holes [2]. Here, we further establish the existence of another regular black hole solution, particularly the D-dimensional extension of the Dymnikova black hole, within the equations of motion incorporating an infinite tower of higher-curvature corrections. This solution is essentially nonperturbative in the coupling parameter, rendering the action, if it exists, incapable of being approximated by a finite number of powers of the curvature. In addition, we compute the dominant quasinormal frequencies of such black holes using both the Bernstein polynomial method and the 13th order WKB method with Padé approximants, obtaining a high degree of agreement between them.

中文翻译：

---

来自高曲率修正无限塔的迪姆尼科娃黑洞


最近，在[1]中，人们证明了可以在一个理论中导出各种规则的黑洞度量，该理论对广义相对论具有无限数量的更高曲率修正。此外，在前几阶截断这个无限级数已经产生了此类黑洞可观测特征的可靠近似值[2]。在这里，我们进一步确定了另一个规则黑洞解的存在，特别是 Dymnikova 黑洞的 D 维扩展，在包含更高曲率修正的无限塔的运动方程中。该解在耦合参数方面本质上是非微扰的，使得作用（如果存在）无法用有限数量的曲率幂来近似。此外，我们还使用 Bernstein 多项式方法和 Padé 近似的 13 阶 WKB 方法计算了此类黑洞的主拟正态频率，获得了它们之间的高度一致性。