Distributional Schwarzschild Geometry from nonsmooth regularization via Horizon. Disributional Rindler spacetime with disributional Levi-Civit`a connection induced vacuum dominance

摘要

In this paper we leave the neighborhood of the singularity at the origin andturn to the singularity at the horizon. Using nonlinear superdistributionalgeometry and supergeneralized functions it seems possible to show that thehorizon singularity is not only a coordinate singularity without leavingSchwarzschild coordinates. However the Tolman formula for the total energy $E$of a static and asymptotically flat spacetime,gives $E=mc^2$, as it should be.New class Colombeau solutions to Einstein field equations is obtained.New classColombeau solutions to Einstein field equations is obtained. The vacuum energydensity of free scalar quantum field $F$ with a distributional backgroundspacetime also is considered.