定常黑洞的边界条件;对Kerr、Martinez-Troncoso-Zanelli和多毛黑洞的应用
Boundary conditions for stationary black holes ; Application to Kerr, Martinez-Troncoso-Zanelli and hairy black holes
摘要：
这项工作提出了一组方程，可用于数值计算时空包含一个固定的黑洞。该方法是基于广义相对论的3+1分解和空间调和规范。黑洞的存在是用平衡态的视视界概念来强化的。这种设置导致本文的主要结果：一组边界条件描述的地平线，必须使用时，解决3+1方程。这些条件导致坐标的选择，即使在地平线本身也是规则的。通过三个不同的算例验证了该方法的有效性。首先，单个旋转的黑洞恢复到非常高的克尔参数值。第二，非旋转黑洞耦合到一个真正的标量场，在存在一个负的宇宙学常数（所谓的MTZ黑洞），得到。最后，计算了具有复杂标量头发的黑洞。最后，未来的工作前景，特别是在平稳性只是近似的情况下，进行了讨论。
英文摘要：
This work proposes a set of equations that can be used to numerically compute spacetimes containing a stationary black hole. The formalism is based on the 3+1 decomposition of General Relativity with maximal slicing and spatial harmonic gauge. The presence of the black hole is enforced using the notion of apparent horizon in equilibrium. This setting leads to the main result of this paper: a set of boundary conditions describing the horizon and that must be used when solving the 3+1 equations. Those conditions lead to a choice of coordinates that is regular even on the horizon itself. The whole procedure is validated with three different examples chosen to illustrate the great versatility of the method. First, the single rotating black holes are recovered up to very high values of the Kerr parameter. Second, non-rotating black holes coupled to a real scalar field, in the presence of a negative cosmological constant (the so-called MTZ black holes), are obtained. Last, black holes with complex scalar hairs are computed. Eventually, prospects for future work, in particular in contexts where stationarity is only approximate, are discussed.
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