Arbitrary compact shapes

"Casimir Forces between Arbitrary Compact Objects,"

T. Emig, N. Graham, R. L. Jaffe, and M. Kardar, Phys. Rev. Lett. 99, 170403 (2007)

Generalizes the multi-pole expansion from electrostatics to fluctuating sources

Full results are available for (frequency-dependent) dielectrics, as well as metals

Can be generalized to arbitrary compact shapes:

The shape and material properties are encoded in the scattering properties of the object.