A canonical foliation on null infinity in perturbations of Kerr

TL;DR

This paper constructs a canonical foliation on null infinity in perturbed Kerr spacetimes, clarifying physical quantities like energy and momentum, and demonstrating large recoil effects on the black hole's center of mass.

Contribution

It establishes a unique, physically meaningful foliation on null infinity in Kerr perturbations, resolving ambiguities in gravitational radiation quantities.

Findings

Existence of a canonical foliation on null infinity in Kerr perturbations.

Physical quantities like energy, momentum, and angular momentum are well-defined and obey expected laws.

Black hole center of mass experiences significant recoil after perturbation.

Abstract

Kerr stability for small angular momentum has been proved in the series of works by Klainerman-Szeftel, Giorgi-Klainerman-Szeftel and Shen. Some of the most basic conclusions of the result, concerning various physical quantities on the future null infinity are derived in the work of Klainerman-Szeftel. Further important conclusions were later derived in An-He-Shen and Chen-Klainerman. In this paper, based on the existence and uniqueness results for GCM spheres by Klainerman-Szeftel, we establish the existence of a canonical foliation on the future null infinity for which the null energy, linear momentum, center of mass and angular momentum are well defined and satisfy the expected physical laws of gravitational radiation. The rigid character of this foliation eliminates the usual ambiguities related to these quantities in the physics literature. We also show that under the initial assumption of Klainerman-Szeftel, the center of mass of the black hole has a large deformation (recoil) after the perturbation.