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

TL;DR

This paper explores the nature of horizon singularities using advanced distributional geometry, introduces new solutions to Einstein's equations, and revisits the Unruh effect, revealing that quantum vacuum energy can dominate classical energy in certain distributional spacetimes.

Contribution

It presents a novel approach to horizon singularities with superdistributional geometry, introduces new Colombeau solutions to Einstein's equations, and revisits quantum effects in distributional backgrounds.

Findings

Horizon singularity is a coordinate singularity in Schwarzschild coordinates.

Vacuum energy can dominate classical energy in distributional Rindler spacetimes.

Quantum vacuum fluctuations become singular at the Rindler horizon.

Abstract

In this paper we leave the neighborhood of the singularity at the origin and turn to the singularity at the horizon. Using nonlinear superdistributional geometry and supergeneralized 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 $E$ 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 class Colombeau solutions to Einstein field equations is obtained. The vacuum energy density of free scalar quantum field ${\Phi}$ with a distributional background spacetime also is considered.It has been widely believed that, except in very extreme situations, the influence of acceleration on quantum fields should amount to just small, sub-dominant contributions. Here we argue that this belief is wrong by showing that in a Rindler distributional background spacetime with distributional Levi-Civit\`a connection the vacuum energy of free quantum fields is forced, by the very same background distributional space-time such a Rindler distributional background space-time, to become dominant over any classical energy density component.This semiclassical gravity effect finds its roots in the singular behavior of quantum fields on a Rindler distributional space-times with distributional Levi-Civit\`a connection. In particular we obtain that the vacuum fluctuations $<{\Phi}^2({\delta})>$ have a singular behavior at a Rindler horizon $\delta = 0$.Therefore sufficiently strongly accelerated observer burns up near the Rindler horizon. Thus Polchinski account does not violate of the Einstein equivalence principle.