Gravitational wave reception by a sphere

Abstract

The reception of gravitational waves by an elastic self-gravitating spherical detector is studied in detail. The equations of motion of a detector driven by a gravitational wave are presented in the intuitively convenient coordinate system of Fermi. An exact analytic solution is given for the homogeneous isotropic sphere. Nonlinear effects of a massive self-gravitating system are computed for a body of mass equal to that of the earth, and are shown to be numerically important.