Explicit solution of the linearized Einstein equations in TT gauge for all multipoles

TL;DR

This paper derives explicit solutions for linearized gravitational waves in TT gauge for all multipoles, extending the known quadrupole case using the Regge-Wheeler-Zerilli formalism.

Contribution

It provides a general explicit metric solution for gravitational waves of any multipole in TT gauge, broadening the applicability of previous quadrupole-focused results.

Findings

Explicit multipole solutions for linearized gravitational waves.

Generalization of the quadrupole solution to all multipoles.

Utilization of the Sarbach and Tiglio formalism for derivation.

Abstract

We write out the explicit form of the metric for a linearized gravitational wave in the transverse-traceless gauge for any multipole, thus generalizing the well-known quadrupole solution of Teukolsky. The solution is derived using the generalized Regge-Wheeler-Zerilli formalism developed by Sarbach and Tiglio.