Distributional Schwarzschild Geometry from Non Smooth Regularization Via Horizon
Jaykov Foukzon *
Center for Mathematical Sciences, Israel Institute of Technology, Haifa, Israel.
*Author to whom correspondence should be addressed.
Abstract
In this paper we leave the neighborhood of the singularity at the origin and turn to the singularity at the horizon. Using nonlinear distributional geometry and Colombeau generalized functions it seems possible to show that the horizon singularity is not only a coordinate singularity without leaving Schwarzschild coordinates. However the Tolman formula for the total energy ET of a static and asymptotically flat spacetime,gives ET = m, as it should be.
Keywords: Colombeau nonlinear generalized functions, Distributional Riemannian Geometry, Distributional Schwarzschild Geometry, Schwarzschild singularity, Schwarzschild Horizon, smooth regularization, nonsmooth regularization.