标题： 黑洞受引力波非线性扰动。 III. 纽曼-彭罗斯常数 显示英文标题

标题： The non-linear perturbation of a black hole by gravitational waves. III. Newman-Penrose constants

摘要： 在本文中，我们继续研究施瓦茨希尔德黑洞对入射引力波的非线性响应，通过计算纽曼-彭罗斯（NP）常数。NP常数是在空无穷远$\mathscr{I}^+$上定义的五个复数、超平移不变量，尽管在60年代就提出了，但在非稳态情况下从未被计算过。我们通过弗里德里希广义共形场方程的数值实现来完成这一任务，其半全局演化直接提供了对$\mathscr{I}+$的访问。对NP常数积分表达式的推广使得它们可以在更适合数值演输出的更一般规范下进行计算。讨论了固定其定义中固有自由度的标准方法。然后在轴对称情况下，针对各种不同的入射波形计算了NP常数，随后在3+1情况下没有任何对称性假设，此时所有五个常数都不为零。 显示英文摘要

摘要： In this paper we continue our study of the non-linear response of a Schwarzschild black hole to an ingoing gravitational wave by computing the Newman-Penrose (NP) constants. The NP constants are five complex, supertranslation-invariant quantities defined on null infinity $\mathscr{I}^+$ and although put forward in the 60's, they have never been computed in a non-stationary setting. We accomplish this through a numerical implementation of Friedrich's generalized conformal field equations whose semi-global evolution yields direct access to $\mathscr{I}+$. Generalizations of the NP constants' integral expressions are made to allow their computation in a more general gauge that better suits the output of a numerical evolution. Canonical methods of fixing inherent degrees of freedom in their definitions are discussed. The NP constants are then computed for a variety of different ingoing wave profiles in axisymmetry, and then with no symmetry assumptions in 3+1 for which all five are non-zero.