Elasticity as a relativistic matter model

The present project studies the statics and dynamics of ideal elastic solids. The underlying theory used takes into account effects from Special and General Relativity. Although such effects will be small in most practical circumstances, there are a number of mathematical and conceptual issttes associated with this theory which require clarification. One of these is the question whether the free boundary value problem connected with the motion of bodies of finite extent is well-posed. This and other related questions are studied.

The relativistic theory of gravity rests on two pillars. One consists in the gravitational field itself, decribed by the curvature of the spacetime continuum. The other pillar is furnished by the models for the different types of matter, described by the so-called energy momentum tensor. The interaction between both these objects is given by the Einstein equations: "Ricci curvature of spacetime = energy momentum tensor" Mathematical relativity studies solutions to these equations or solutions to the equations describing matter in a given spacetime. In the present project we studied ideally elastic material under relativistic conditions, partly in a given gravitational field, and partly in full interaction with the gravitational field ("self-gravitating matter"). We succeeded in solving the following problems: 1.) The initial value problem for the Einstein equations with energy momentum tensor corresponding to elastic matter. 2.) The motion of a relativistic body composed of elastic material with free boundary. 3.) The equilibrium configurations of relativistical elastic matter in rigid rotation. 4.) Static solutions to the Einstein equations with elastic matter.