Contraction of the Schwarzschild Horizon in Radially Falling Frames

Christopher Laforet

doi:10.20944/preprints202303.0512.v6

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preprints.org > physical sciences > theoretical physics > doi: 10.20944/preprints202303.0512.v6

Preprint Article Version 6 Preserved in Portico This version is not peer-reviewed

Contraction of the Schwarzschild Horizon in Radially Falling Frames

Christopher Laforet

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)
Version 6 : Received: 4 September 2023 / Approved: 5 September 2023 / Online: 5 September 2023 (10:01:55 CEST)
Version 7 : Received: 8 November 2023 / Approved: 9 November 2023 / Online: 9 November 2023 (14:49:33 CET)
Version 8 : Received: 3 December 2023 / Approved: 4 December 2023 / Online: 5 December 2023 (09:16:27 CET)
Version 9 : Received: 24 January 2024 / Approved: 25 January 2024 / Online: 5 February 2024 (15:19:21 CET)
Version 10 : Received: 10 March 2024 / Approved: 11 March 2024 / Online: 11 March 2024 (13:23:27 CET)

How to cite: Laforet, C. Contraction of the Schwarzschild Horizon in Radially Falling Frames. Preprints 2023, 2023030512. https://doi.org/10.20944/preprints202303.0512.v6 Laforet, C. Contraction of the Schwarzschild Horizon in Radially Falling Frames. Preprints 2023, 2023030512. https://doi.org/10.20944/preprints202303.0512.v6

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MDPI and ACS Style

Laforet, C. Contraction of the Schwarzschild Horizon in Radially Falling Frames. Preprints 2023, 2023030512. https://doi.org/10.20944/preprints202303.0512.v6

APA Style

Laforet, C. (2023). Contraction of the Schwarzschild Horizon in Radially Falling Frames. Preprints. https://doi.org/10.20944/preprints202303.0512.v6

Chicago/Turabian Style

Laforet, C. 2023 "Contraction of the Schwarzschild Horizon in Radially Falling Frames" Preprints. https://doi.org/10.20944/preprints202303.0512.v6

Abstract

A new coordinate system based on the proper times of rest frames in the Schwarzschild metric is developed to show that a radially falling worldline becomes light-like at the event horizon in the Schwarzschild metric. This system has no coordinate singularity at the event horizon and light travels on 45 degree lines everywhere in the space. The light-like nature of the worldline is confirmed by analyzing it in Kruskal-Szekeres (KS) coordinates. It is shown that the worldline in KS coordinates has an undefined derivative at the horizon at any point other than the origin of the KS coordinates. It is then demonstrated that the origin of the KS coordinate system can be reached in the falling frame by exploiting the time symmetry of the manifold and that the falling worldline is indeed light-like there. The light-like nature of the worldline means that the horizon is length contracted to a point in the falling frame, such that the event horizon is proven to be the source of the Schwarzschild metric and the end point of gravitational collapse.

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.

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Comments (1)

Comment 1

Received: 5 September 2023
Commenter: Christopher Laforet
Commenter's Conflict of Interests: Author

Comment: - Chagned title
- Added new coordinate transformation
- Removed density discussion

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