特殊时空波动方程的CMC切片和定序保角紧化数值解
Numerical solution of the wave equation on particular space-times using CMC slices and scri-fixing conformal compactification
摘要：
本文详细地给出了对应于两种不同情况的固定背景时空上的共形不变波动方程的数值解：i）笛卡尔坐标下的1+1 Minkowski时空和ii）Schwarzschild时空。在这两种情况下，我们使用双曲常平均曲率切片和scri-fixing共形紧化，并求解共形时空上的波动方程。在Schwarzschild时空中，我们研究了无质量标量场对应的准正规模振荡和后时间多项式尾衰减指数。我们还提出了一般公式来构造双曲常平均曲率切片的球对称，静态，时空在球坐标系。
英文摘要：
In this paper we present in detail the numerical solution of the conformally invariant wave equation on top of a fixed background space-time corresponding to two different cases: i) 1+1 Minkowski space-time in Cartesian coordinates and ii) Schwarzschild space-time. In both cases we use hyperboloidal constant mean curvature slices and scri-fixing conformal compactification, and solve the wave equation on the conformal space-time. In the case of the Schwarzschild space-time we study the quasinormal mode oscillations and the late-time polynomial tail decay exponents corresponding to a mass-less scalar field. We also present general formulas to construct hyperboloidal constant mean curvature slicings of spherically symmetric, static, space-times in spherical coordinates.
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