Black Hole Construction from the Minkowski Manifold

Christopher Laforet

doi:10.20944/preprints202303.0512.v7

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preprints.org > physical sciences > theoretical physics > doi: 10.20944/preprints202303.0512.v7

Preprint Article Version 7 Preserved in Portico This version is not peer-reviewed

Black Hole Construction from the Minkowski Manifold

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. Black Hole Construction from the Minkowski Manifold. Preprints 2023, 2023030512. https://doi.org/10.20944/preprints202303.0512.v7 Laforet, C. Black Hole Construction from the Minkowski Manifold. Preprints 2023, 2023030512. https://doi.org/10.20944/preprints202303.0512.v7

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MDPI and ACS Style

Laforet, C. Black Hole Construction from the Minkowski Manifold. Preprints 2023, 2023030512. https://doi.org/10.20944/preprints202303.0512.v7

APA Style

Laforet, C. (2023). Black Hole Construction from the Minkowski Manifold. Preprints. https://doi.org/10.20944/preprints202303.0512.v7

Chicago/Turabian Style

Laforet, C. 2023 "Black Hole Construction from the Minkowski Manifold" Preprints. https://doi.org/10.20944/preprints202303.0512.v7

Abstract

The Schwarzschild manifold is constructed by taking a point on the Minkowski manifold and stretching it into a 4-sphere. This stretch causes gradients in the temporal and spatial coordinate densities around the sphere, leaving a hole of null space-time in the manifold centered at the spatial location of the original point. It is shown that this accurately models the Schwarzschild metric and is used to prove that radial infalling geodesics become null at the horizon and come to rest there. 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: 9 November 2023
Commenter: Christopher Laforet
Commenter's Conflict of Interests: Author

Comment: - Updated title and abstract
- Added a section on constructing black holes by stretching a point in Minkowski spacetime into a 4-sphere

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