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

Understand

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.