Bi-orthogonal harmonics for the decomposition of gravitational radiation I: angular modes, completeness, and the introduction of adjoint-spheroidal harmonics

Understand

The estimation of radiative modes is a central problem in gravitational wave theory, with essential applications in signal modeling and data analysis.

• This problem is complicated by most astrophysically relevant systems' not having modes that are analytically tractable.
• A ubiquitous workaround is to use not modes, but multipole moments defined by spin weighted spherical harmonics.
• However, spherical multipole moments are only related to the modes of systems without angular momentum.