A four-dimensional regularization of Lovelock–Lanczos gravity up to an arbitrary curvature order is considered. We show that Lovelock–Lanczos terms can provide a non-trivial contribution to the Einstein field equations in four dimensions, for spherically symmetric and Friedmann–Lemaître–Robertson–Walker spacetimes, as well as at first order in perturbation theory around (anti) de Sitter vacua. We will discuss the cosmological and black hole solutions arising from these theories, focusing on the presence of attractors and their stability. Although curvature singularities persist for any finite number of Lovelock terms, it is shown that they disappear in the non-perturbative limit of a theory with a unique vacuum.

可以考虑对Lovelock-Lanczos重力进行四维正则化，直至任意曲率阶。我们证明，对于球对称和Friedmann-Lemaître-Robertson-Walker时空，以及在（anti）de周围的扰动理论中，洛夫洛克-兰佐斯项可以在四个维度上为爱因斯坦场方程提供非平凡的贡献。保姆真空。我们将讨论由这些理论引起的宇宙学和黑洞解决方案，重点是吸引子的存在及其稳定性。尽管曲奇奇点在任意数量的Lovelock项中都存在，但可以证明它们在具有唯一真空的理论的非摄动极限中消失了。