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.
Highlights
In March 2012, Joseph Polchinski claimed that the following three statements cannot all be true [1]: 1) Hawking radiation is in a pure state, 2) the information carried by the radiation is emitted from the region near the horizon, with low energy effective field theory valid beyond some microscopic distance from the horizon, 3) the infalling observer encounters nothing unusual at the horizon
We argue that this belief is wrong by showing that in a Rindler distributional background space-time with distributional Levi-Cività 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-Cività connection
Summary
In March 2012, Joseph Polchinski claimed that the following three statements cannot all be true [1]: 1) Hawking radiation is in a pure state, 2) the information carried by the radiation is emitted from the region near the horizon, with low energy effective field theory valid beyond some microscopic distance from the horizon, 3) the infalling observer encounters nothing unusual at the horizon. Joseph Polchinski argues that the most conservative resolution is: the infalling observer burns up at the horizon. In Polchinski’s account, quantum effects would turn the event horizon into a seething maelstrom of particles. Anyone who fell into it would hit a wall of fire and be burned to a crisp in an instant. In this paper we argue that Polchinski was not wrong, but Unruh effect revision is needed
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