Abstract

The conformal field equations, black holes, gravitational waves and the Newman-Penrose constants

In recent years, a (numerically) wellposed Initial Boundary Value Problem (IBVP) for the generalized conformal field equations has been put forward. These equations regularly extend the Einstein equations to include “infinity” and the associated IBVP has been used to successfully evolve, in the fully non-linear regime, a black hole space-time perturbed with a gravitational wave. This framework allows for direct calculations of global quantities defined at infinity, such as the Bondi-Sachs energy-momentum, and we have used it to successfully reproduce the Bondi-Sachs mass loss.

In this talk, two applications will be discussed:

Linear perturbations of black holes are well known and the associated oscillations in the Weyl curvature are known as quasinormal modes. In recent work, we investigated the analogous non-linear curvature oscillations and how they decay to the linear regime. In doing so, we have observed that only a short amount of physical proper time can be resolved numerically in the conformal representation. Ideas to alleviate this problem will be put forward.

Another recent application was the calculation of the Newman-Penrose Constants (NPC). These are five complex quantities defined on null infinity that are absolutely conserved if it is smooth. In stationary space-times, they can be written terms of mass and angular momentum moments, but their physical interpretation in non-stationary space-times is still lacking. We compute, for the first time, the NPC in a general setting and show that they remain constant, implying smoothness of null infinity to at least the level of our numerical precision.