We discuss foundational issues of Lorentzian geometry and General Relativity for metrics of low regularity. In particular, we recall the distributional approach due to Geroch, Traschen and LeFloch, Mardare and discuss its merits and limitations. Then we present a more general approach based on the nonlinear extension of distribution theory due to Colombeau. We discuss this nonlinear distributional Lorentzian geometry in some detail and address several applications in General Relativity as well as its compatibility with the purely distributional picture.
Abstract: In this talk, a class of static spherically symmetric solutions of the general relativistic elasticity equations is discussed . The main point of the discussion is the comparison of two matter models given in terms of their stored energy functionals, i.e., the rule which gives the amount of energy stored in the system when it is deformed. Both functionals mimic (and for small deformations approximate) the classical Kirchhoff–St Venant materials but differ in the strain variable used. We discuss the behavior of the systems for large deformations.