Non-radial pulsations of neutron stars with a crust

Summary A fully relativistic treatment of non-radial pulsational modes of spherical stars with solid crusts is presented. This work complements Schumaker & Thorne’s relativistic treatment of torsional modes. The strain tensor for arbitrary even-parity elastic deformations of a spherical star is derived. A Hookean law is assumed to relate the stress to the strain, and the pulsational equations and their boundary condition; are derived from the Einstein Field Equations (EFE) and the equations of motion. The EFE and equations of motion are then used to find the Lagrangian density and an action principle for the pulsational problem. This action principle may prove useful in future studies of the stability of non-radial pulsational modes for stars with a solid crust.