A GENERALIZATION OF THE RELATIVISTIC EQUILIBRIUM EQUATIONS FOR A NONROTATING STAR

The problem of elastomechanical equilibrium for a static, spherically symmetric star composed of an elastic material is analyzed. A suitable formulation of relativistic elasticity theory is used, and the second order equilibrium equations are found. It is shown that the equilibrium conditions with "anisotropic pressure" introduced ad hoc by some authors are in fact the dynamical conditions for a relativistic elastic material. The corresponding first order equations for the components of the metric and of the energy-momentum tensor reduce to the Tolman-Oppenheimer-Volkhoff equations if the material exhibits no shape-rigidity. Two interesting classes of solutions are discussed.