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How to cite:
Laforet, C. Examination of the Event Horizon and Internal Geometry of the Schwarzschild Metric in Kruskal-Szekeres Coordinates. Preprints2023, 2023030512. https://doi.org/10.20944/preprints202303.0512.v3
Laforet, C. Examination of the Event Horizon and Internal Geometry of the Schwarzschild Metric in Kruskal-Szekeres Coordinates. Preprints 2023, 2023030512. https://doi.org/10.20944/preprints202303.0512.v3
Laforet, C. Examination of the Event Horizon and Internal Geometry of the Schwarzschild Metric in Kruskal-Szekeres Coordinates. Preprints2023, 2023030512. https://doi.org/10.20944/preprints202303.0512.v3
APA Style
Laforet, C. (2023). Examination of the Event Horizon and Internal Geometry of the Schwarzschild Metric in Kruskal-Szekeres Coordinates. Preprints. https://doi.org/10.20944/preprints202303.0512.v3
Chicago/Turabian Style
Laforet, C. 2023 "Examination of the Event Horizon and Internal Geometry of the Schwarzschild Metric in Kruskal-Szekeres Coordinates" Preprints. https://doi.org/10.20944/preprints202303.0512.v3
Abstract
It is demonstrated mathematically that the Schwarzschild radius is the end point of gravitational collapse using the definitions of the Kruskal-Szekeres coordinates and their relationship to the Schwarzschild coordinate basis vectors over the coordinate chart. The extrinsic nature of the Kruskal-Szekeres coordinates obscures the asymptote that separates the internal and external spacetimes at the horizon. It is proven that all observers that hypothetically reach the horizon are coincident with each other at the horizon, regardless of where or when they began falling relative to each other. It is also proven that all worldlines become null geodesics at the event horizon in Kruskal-Szekeres coordinates and intersect the point T=X=0 there. In the frame of falling observers, the event horizon relativistically contracts to zero size as the horizon is approached. The internal solution is describing a spherically symmetric vacuum surrounded by an infinitely dense shell that is infinitely far away in space and exists a finite time in the past relative to an observer in the vacuum.
Keywords
Black holes; General Relativity; Schwarzschild metric
Subject
Physical Sciences, Theoretical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Commenter: Christopher Laforet
Commenter's Conflict of Interests: Author