Perturbations of a Schwarzschild black hole and Newman-Unti gauge

Abstract

In this paper, we derive the complete transformations of a generic first order perturbative metric in Schwarzschild spacetime to the Newman-Unti (NU) gauge in series expansion near null infinity. This allows us to determine the asymptotic shear, the mass aspect and the angular momentum aspect of the perturbative fields. As a direct application, we derive the corresponding asymptotic NU data for quasinormal modes (QNMs) of a Schwarzschild black hole. The total energy and angular momentum of QNMs obtained from the asymptotic NU data vanish but classical supertranslation charges are non-trivial, which can be applied to fix the BMS frame at first perturbative order.