论文标题
固定黑洞的边界条件；应用于Kerr，Martinez-Troncoso-Zanelli和毛茸茸的黑洞
Boundary conditions for stationary black holes ; Application to Kerr, Martinez-Troncoso-Zanelli and hairy black holes
论文作者
论文摘要
这项工作提出了一组方程，可用于数值计算固定黑洞的空间。形式主义基于最大切片和空间谐波仪的一般相对性的3+1分解。黑洞的存在是使用平衡中明显范围的概念来实现的。此设置导致本文的主要结果：一组描述地平线的边界条件，在求解3+1方程时必须使用。这些条件会导致坐标的选择，即使在地平线本身也是规律的。整个过程通过选择的三个不同示例验证，以说明该方法的多功能性。首先，将单个旋转黑洞恢复到KERR参数的很高值。其次，在存在负宇宙常数（所谓的MTZ黑洞）的情况下，无旋转的黑洞与真实的标量耦合。最后，计算带有复杂标质头发的黑洞。最终，讨论了未来工作的前景，尤其是在仅近似平稳性的情况下。
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.
