标题： Lovelock黑洞中的卡斯纳时代 显示英文标题

标题： Kasner eons in Lovelock black holes

摘要： 在类空奇点附近，广义相对论预测度规在每一点的行为都类似于一个Kasner空间，该空间经历一系列由特定转换规则定义的“Kasner时代”和“时期”。这个过程发生的时间段定义了一个“Kasner纪元”，当高曲率或量子效应变得相关时，该纪元结束。当作用量中包含高曲率密度时，时空可以过渡到额外的Kasner纪元。在每个纪元内，度规在局域上表现为由控制动力学的高曲率密度决定的Kasner解。本文我们识别了静态且球对称的Lovelock引力黑洞内部存在的Kasner纪元。我们确定了纪元发生的条件，并研究了表征它们的Kasner度规以及它们之间的转换。我们证明，无能动量条件意味着爱因斯坦纪元末尾的有效Kasner指数具有单调性属性。我们还描述了更一般的高曲率引力理论的Kasner解。特别是，我们观察到爱因斯坦引力条件（Kasner指数之和等于1，即$\sum_{i=1}^{D-1}p_i=1$）可以推广为一族满足$\sum_{i=1}^{D-1}p_i=2n -1$的Kasner度规，这些度规对于任意阶$n$高曲率密度和一般维度都存在。 显示英文摘要

摘要： In the vicinity of space-like singularities, general relativity predicts that the metric behaves, at each point, as a Kasner space which undergoes a series of "Kasner epochs" and "eras" characterized by certain transition rules. The period during which this process takes place defines a "Kasner eon", which comes to an end when higher-curvature or quantum effects become relevant. When higher-curvature densities are included in the action, spacetime can undergo transitions into additional Kasner eons. During each eon, the metric behaves locally as a Kasner solution to the higher-curvature density controlling the dynamics. In this paper we identify the presence of Kasner eons in the interior of static and spherically symmetric Lovelock gravity black holes. We determine the conditions under which eons occur and study the Kasner metrics which characterize them, as well as the transitions between them. We show that the null energy condition implies a monotonicity property for the effective Kasner exponent at the end of the Einsteinian eon. We also characterize the Kasner solutions of more general higher-curvature theories of gravity. In particular, we observe that the Einstein gravity condition that the sum of the Kasner exponents adds up to one, $\sum_{i=1}^{D-1}p_i=1$, admits a universal generalization in the form of a family of Kasner metrics satisfying $\sum_{i=1}^{D-1}p_i=2n -1$ which exists for any order-$n$ higher-curvature density and in general dimensions.