Charges for linearized gravity

TL;DR

This paper investigates non-radiating modes in linearized gravity on Kerr spacetime, linking them to conserved charges and explicitly calculating the linearized mass charge using Newman-Penrose scalars.

Contribution

It identifies gauge-invariant non-radiating modes related to the Poincare algebra and computes the linearized mass charge in terms of Newman-Penrose scalars.

Findings

Non-radiating modes correspond to infinitesimal perturbations of mass and angular momentum.

Linearized mass charge is explicitly expressed via Newman-Penrose scalars.

Kerr's isometry group relates to gauge-invariant non-radiating modes.

Abstract

Maxwell test fields as well as solutions of linearized gravity on the Kerr exterior admit non-radiating modes, i.e. non-trivial time-independent solutions. These are closely related to conserved charges. In this paper we discuss the non-radiating modes for linearized gravity, which may be seen to correspond to the Poincare Lie-algebra. The 2-dimensional isometry group of Kerr corresponds to a 2-parameter family of gauge-invariant non-radiating modes representing infinitesimal perturbations of mass and azimuthal angular momentum. We calculate the linearized mass charge in terms of linearized Newman-Penrose scalars.