A Hypercontinuous Hypersmooth, Scharzschild Line Element Transformation
Robert A. Herrmann
TL;DR
This paper applies nonstandard analysis to the Schwarzschild metric to address singularities and explores the evolution of near-horizon gravitational collapse.
Contribution
It introduces a hypercontinuous, hypersmooth transformation of the Schwarzschild line element using nonstandard analysis techniques.
Findings
Singularities can be mitigated through nonstandard analysis transformations.
The evolution of collapsing bodies near the Schwarzschild radius is characterized.
The approach offers a new perspective on black hole horizon behavior.
Abstract
In this paper, the Eddington-Finkelstein transformation is used as an illustration of how the problem of singularities or infinities can be removed by application of nonstandard analysis to the Schwarzschild line element (metric). The evolution of a gravitationally collapsing spherical body with radius greater than but near to the Schwarzschild radius is also investigated.
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Taxonomy
TopicsMathematical and Theoretical Analysis · History and Theory of Mathematics · Mathematics and Applications