Tensorial Spin-s Harmonics

TL;DR

This paper introduces a method to define tensorial spin-s harmonics from spin-s spherical harmonics, providing useful tools for calculations in General Relativity involving tensor functions on the sphere.

Contribution

It presents a systematic way to derive tensorial spin-s harmonics from spin-s spherical harmonics and provides their decompositions, facilitating complex calculations in gravitational physics.

Findings

Defined tensorial spin-s harmonics from spin-s spherical harmonics

Provided decomposition formulas for tensorial spin-s harmonics

Demonstrated usefulness in General Relativity calculations

Abstract

We show how to define and go from the spin-s spherical harmonics to the tensorial spin-s harmonics. These quantities, which are functions on the sphere taking values as Euclidean tensors, turn out to be extremely useful for many calculations in General Relativity. In the calculations, products of these functions, with their needed decompositions which are given here, often arise naturally.