Beyond the Spherical Cow: A Full Multipole Expansion

Higher Multipoles of the Cow

The spherical cow approximation, a staple of theoretical physics, is rarely justified. This paper extends it into a full multipole expansion, treating the spherical cow as the first term. This enables computation of bovine potentials and interactions beyond spherical symmetry and defines the cow's geometry at higher multipole moments. The author demonstrates the calculation of multipole coefficients for a benchmark cow and applies the multipolar cow to problems like gravitational-wave spindown of a rotating cow.