A strained space-time

A. Tartaglia

Space-time can be described as a four-dimensional manifold with properties similar to the ones of a material continuum. In particular if the manifold is curved its metric properties can be expressed in terms of a strained state introduced in a previously unstrained and flat reference manifold. We present a theory based on this analogy, where the strain tensor of a curved manifold is given as the non trivial part of the metric tensor. The Lagrangian density of the empty, but curved, space-time, is extended to include an “elastic” potential energy density, due to the presence of strain. The theory has been tested at the cosmological scale, being applied to the primordial nucleosynthesis, the structure formation in the universe and the luminosity of the type Ia supernovae. The results have been satisfactory. The same approach has been also adopted for the typical Schwarzschild symmetry leading to changes in the propagation of light in the field of a spherical mass, that are unperceivable at the scale of the Solar system. After presenting the theory, its perspectives will be discussed.