Tensor Harmonics in Canonical Form for Gravitational Radiation and Other Applications

Abstract

An analysis is made of the relation between the tensor harmonics given by Regge and Wheeler in 1957 and those given by Jon Mathews in 1962. This makes it possible to use the Regge‐Wheeler harmonics, which are given in terms of derivatives of scalar spherical harmonics, for calculations while using Mathews' form of the harmonics [linear combinations of the elements of the product basis formed from a basis for scalar functions on the 2‐sphere and a basis for symmetric tensors such that the product basis is split into sets which transform under the irreducible representations of SO(3)] to elucidate the properties of tensor harmonics. Thus, a convenient orthonormal set of harmonics is given which is useful in studying, for example, gravitational radiation.