Version 1
: Received: 28 March 2023 / Approved: 29 March 2023 / Online: 29 March 2023 (14:31:46 CEST)
Version 2
: Received: 12 April 2023 / Approved: 13 April 2023 / Online: 13 April 2023 (12:54:36 CEST)
Version 3
: Received: 1 May 2023 / Approved: 4 May 2023 / Online: 4 May 2023 (11:42:02 CEST)
Version 4
: Received: 10 May 2023 / Approved: 11 May 2023 / Online: 11 May 2023 (14:15:52 CEST)
Version 5
: Received: 30 May 2023 / Approved: 31 May 2023 / Online: 31 May 2023 (13:23:04 CEST)
How to cite:
Laforet, C. Kruskal-Szekeres Coordinates as Extrinsic Coordinates of the Schwarzschild Metric. Preprints.org2023, 2023030512. https://doi.org/10.20944/preprints202303.0512.v1
Laforet, C. Kruskal-Szekeres Coordinates as Extrinsic Coordinates of the Schwarzschild Metric. Preprints.org 2023, 2023030512. https://doi.org/10.20944/preprints202303.0512.v1
Cite as:
Laforet, C. Kruskal-Szekeres Coordinates as Extrinsic Coordinates of the Schwarzschild Metric. Preprints.org2023, 2023030512. https://doi.org/10.20944/preprints202303.0512.v1
Laforet, C. Kruskal-Szekeres Coordinates as Extrinsic Coordinates of the Schwarzschild Metric. Preprints.org 2023, 2023030512. https://doi.org/10.20944/preprints202303.0512.v1
Abstract
It is demonstrated that the Kruskal-Szekeres coordinates are extrinsic coordinates of the Schwarzschild metric while the Schwarzschild coordinates are intrinsic. The is the reason the two coordinate systems treat the event horizon of the metric differently. Since the Kruskal-Szekeres coordinates are extrinsic, they obscure the asymptote that separates the internal and external spacetimes at the horizon. It is proven that all falling 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. 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.
