1301.2231 (Ovidiu Cristinel Stoica)

Singular Semi-Riemannian Geometry and Singular General Relativity    [PDF]

Ovidiu Cristinel Stoica

This work collects a number of results in Singular Semi-Riemannian Geometry and Singular General Relativity. An extension of differential geometry and of Einstein's equation to singularities is reported. Singularities of the form studied here allow a smooth extension of the Einstein field equations, including matter. This applies to the Big-Bang singularity of the FLRW solution. It applies to stationary black holes, in appropriate coordinates (since the standard coordinates are singular, hiding the smoothness of the metric). In these coordinates, charged black holes have the electromagnetic potential regular everywhere. Implications on Penrose's Weyl curvature hypothesis are presented. In addition, these singularities exhibit a (geo)metric dimensional reduction, which acts as a regulator for the quantum fields, including for quantum gravity, in the UV regime.

View original: http://arxiv.org/abs/1301.2231