Higher Multipoles of the Cow

The spherical cow approximation is widely used in the literature, but is rarely justified. Here, I propose several schemes for extending the spherical cow approximation to a full multipole expansion, in which the spherical cow is simply the first term. This allows for the computation of bovine potentials and interactions beyond spherical symmetry, and also provides a scheme for defining the geometry of the cow itself at higher multipole moments. This is especially important for the treatment of physical processes that are suppressed by spherical symmetry, such as the spindown of a rotating cow due to the emission of gravitational waves.

I demonstrate the computation of multipole coefficients for a benchmark cow, and illustrate the applicability of the multipolar cow to several important problems. ar Xiv Labs is a framework that allows collaborators to develop and share new ar Xiv features directly on our website. Both individuals and organizations that work with ar Xiv Labs have embraced and accepted our values of openness, community, excellence, and user data privacy. ar Xiv is committed to these values and only works with partners that adhere to them.

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