Multipole expansions for energy and momenta carried by gravitational waves

TL;DR

This paper derives unified formulas for calculating the energy, momentum, and angular momentum carried by gravitational waves using spin-weighted spherical harmonics, applicable to numerical simulations.

Contribution

It provides a consistent framework that unifies various existing expressions for gravitational wave energy and momentum calculations, applicable to numerical data.

Findings

Derived explicit formulas for energy, momentum, and angular momentum from gravitational waves.

Showed equivalence of new formulas with traditional perturbation methods.

Applicable to numerical simulations for gravitational wave analysis.

Abstract

We present expressions for the energy, linear momentum and angular momentum carried away from an isolated system by gravitational radiation based on spin-weighted spherical harmonics decomposition of the Weyl scalar $\Psi_4$. We also show that the expressions derived are equivalent to the common expressions obtained when using a framework based on perturbations of a Schwazschild background. The main idea is to collect together all the different expressions in a uniform and consistent way. The formulae presented here are directly applicable to the calculation of the radiated energy, linear momentum and angular momentum starting from the gravitational waveforms which are typically extracted from numerical simulations.