"Peeling property" for linearized gravity in null coordinates

TL;DR

This paper provides a gauge-independent, quasilocal description of linearized gravity in null coordinates, extending previous results, analyzing axial fields, and proving a peeling property at null infinity.

Contribution

It introduces a comprehensive gauge-independent framework for linearized gravity, including a generalized wave equation and peeling property analysis in null coordinates.

Findings

Gauge-independent quasilocal quantities for linearized gravity.

Generalized wave equations including Regge-Wheeler for axial modes.

Proved strong peeling property at null infinity.

Abstract

A complete description of the linearized gravitational field on a flat background is given in terms of gauge-independent quasilocal quantities. This is an extension of the results from gr-qc/9801068. Asymptotic spherical quasilocal parameterization of the Weyl field and its relation with Einstein equations is presented. The field equations are equivalent to the wave equation. A generalization for Schwarzschild background is developed and the axial part of gravitational field is fully analyzed. In the case of axial degree of freedom for linearized gravitational field the corresponding generalization of the d'Alembert operator is a Regge-Wheeler equation. Finally, the asymptotics at null infinity is investigated and strong peeling property for axial waves is proved.