Interaction of Gravitational Waves with Superconductors

Applying the Helmholtz Decomposition theorem to linearized General Relativity leads to a gauge-invariant formulation where the transverse-traceless part of the metric perturbation describes gravitational waves in matter. Gravitational waves incident on a superconductor can be described by a linear London-like constituent equation characterized by a ``gravitational shear modulus'' and a corresponding plasma frequency and penetration depth. It is shown that in the DC limit, the gravitational wave field is expelled from the superconductor in a gravitational Meissner-like effect.