极值正则黑洞的形成
Formation of extremal regular black holes
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中文总结 AI 辅助
本文构造广义准拓扑引力下的正则黑洞几何模型，利用其Vaidya解的二维动力学框架，在不违背能量条件下模拟极值正则黑洞的渐近形成，测地线散焦由修正引力动力学触发。
中文摘要 AI 辅助
具有非极值内视界的静态及缓慢演化的正则黑洞通常会发生质量通胀。本文考虑渐近引力坍缩形成极值正则黑洞（作为候选永恒终态）的场景。为此，我们首先构造了静态球对称单视界极值正则黑洞与双视界内极值正则黑洞的几何模型，其中黑洞质量是唯一的有量纲标度。这些时空可被视为修正引力理论的非微调真空解，该理论的定义要求其球对称约化可得到可积的二维Horndeski理论。这类被称为广义准拓扑引力的理论容许精确的Vaidya解，其中质量为时间的函数。我们利用这一有效的二维二阶动力学框架，在不违背能量条件的情况下，模拟极值正则黑洞的渐近形成。这一点通过以下等价关系得到明确体现：广义相对论的广义Vaidya解的强能量条件，与运动学类时收敛条件在动力学上被重新表述为关于球对称约化的理论相关函数的壳上条件，对应于广义准拓扑引力的Vaidya解。正则黑洞所需的测地线散焦因此由修正引力动力学触发，而非通过引入奇异物质自由度实现。
英文摘要
Static and slowly evolving regular black holes with a non-extremal inner horizon are generally expected to suffer from mass inflation. Here we consider the scenario of asymptotic gravitational collapse into extremal regular black holes. To that end, we first construct geometric models of static spherically symmetric single-horizon extremal and double-horizon inner-extremal regular black holes for generic black hole mass as the only dimensionful scale. These spacetimes may be interpreted as non-fine-tuned vacuum solutions of modified gravitational theories defined implicitly by the requirement that their spherical reduction yields an integrable two-dimensional Horndeski theory. As such, these so-called general quasi-topological gravities admit exact Vaidya solutions in which the mass becomes a time-dependent function. We use this effectively two-dimensional second-order dynamical framework to model the asymptotic formation of extremal regular black holes without a violation of energy conditions. The latter is illustrated explicitly by the equivalence between the strong energy condition for generalised Vaidya solutions of general relativity, and the kinematic timelike convergence condition reformulated dynamically as an onshell condition on the theory-dependent functions characterising the spherical reduction and correspondingly Vaidya solutions of a general quasi-topological gravity. The defocusing of geodesics necessary for regular black holes is thus triggered by the modified gravitational dynamics rather than by the addition of exotic matter degrees of freedom.
