Lorentz Boosts and Rapidity for Inertial Observers in Kruskal-Szekeres Coordinates

Christopher Laforet

doi:10.20944/preprints202303.0512.v5

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preprints.org > physical sciences > theoretical physics > doi: 10.20944/preprints202303.0512.v5

Preprint Article Version 5 Preserved in Portico This version is not peer-reviewed

Lorentz Boosts and Rapidity for Inertial Observers in Kruskal-Szekeres Coordinates

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. Lorentz Boosts and Rapidity for Inertial Observers in Kruskal-Szekeres Coordinates. Preprints 2023, 2023030512. https://doi.org/10.20944/preprints202303.0512.v5 Laforet, C. Lorentz Boosts and Rapidity for Inertial Observers in Kruskal-Szekeres Coordinates. Preprints 2023, 2023030512. https://doi.org/10.20944/preprints202303.0512.v5

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MDPI and ACS Style

Laforet, C. Lorentz Boosts and Rapidity for Inertial Observers in Kruskal-Szekeres Coordinates. Preprints 2023, 2023030512. https://doi.org/10.20944/preprints202303.0512.v5

APA Style

Laforet, C. (2023). Lorentz Boosts and Rapidity for Inertial Observers in Kruskal-Szekeres Coordinates. Preprints. https://doi.org/10.20944/preprints202303.0512.v5

Chicago/Turabian Style

Laforet, C. 2023 "Lorentz Boosts and Rapidity for Inertial Observers in Kruskal-Szekeres Coordinates" Preprints. https://doi.org/10.20944/preprints202303.0512.v5

Abstract

The Lorentz boost and rapidity for a radially falling frame are derived for the Schwarzschild metric in Kruskal-Szekeres coordinates. It is found through this analysis that the spacetime is radially length contracted toward the metric source in the falling frame as a result of the Lorentz boosting relative to the rest frame (which is shown to be consistent with the rest frame). When the falling frame reaches the event horizon, the Lorentz boost goes to infinity, causing the falling frame to become light-like, but trapped at the horizon. It is shown that in the falling frame at the horizon, the density of the source goes to infinity as a result of the length contraction.

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: 31 May 2023
Commenter: Christopher Laforet
Commenter's Conflict of Interests: Author

Comment: - Updated title
- Updated abstract
- Condensed the paper into 4 pages
- Removed the discussion on symmetries
- Focused on the mathematics of Lorentz boosts and rapidity in Kruskal-Szekeres coordinates

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