Preprint Article Version 6 Preserved in Portico This version is not peer-reviewed

Extended Field Equations for Conformally Curved Spacetime

Version 1 : Received: 15 October 2020 / Approved: 15 October 2020 / Online: 15 October 2020 (11:47:59 CEST)
Version 2 : Received: 18 October 2020 / Approved: 19 October 2020 / Online: 19 October 2020 (10:43:06 CEST)
Version 3 : Received: 5 November 2020 / Approved: 6 November 2020 / Online: 6 November 2020 (13:11:37 CET)
Version 4 : Received: 1 January 2021 / Approved: 4 January 2021 / Online: 4 January 2021 (11:21:08 CET)
Version 5 : Received: 17 June 2021 / Approved: 17 June 2021 / Online: 17 June 2021 (14:08:56 CEST)
Version 6 : Received: 18 November 2021 / Approved: 18 November 2021 / Online: 18 November 2021 (13:17:29 CET)

How to cite: Al-Fadhli, M.B. Extended Field Equations for Conformally Curved Spacetime. Preprints 2020, 2020100320 (doi: 10.20944/preprints202010.0320.v6). Al-Fadhli, M.B. Extended Field Equations for Conformally Curved Spacetime. Preprints 2020, 2020100320 (doi: 10.20944/preprints202010.0320.v6).

Abstract

The recent Planck Legacy release has confirmed the presence of an enhanced lensing amplitude in the cosmic microwave background power spectra, which prefers a positively curved early Universe with a confidence level greater than 99%. In addition, the spacetime curvature of the entire galaxy differs from one galaxy to another due to their diverse energy densities. This study considers both the implied positive curvature of the early Universe and the curvature across the entire galaxy as the curvature of ‘the background or the 4D bulk’ and distinguishes it from the localized curvature that is induced in the bulk by the presence of comparably smaller celestial objects that are regarded as ‘relativistic 4D branes’. Branes in different galaxies experience different bulk curvatures, thus their background or bulk curvature should be taken into consideration along with their energy densities when finding their induced curvatures. To account for the interaction between the bulk and branes, this paper presents extended field equations in terms of brane-world modified gravity consisting of conformal Einstein field equations with a boundary term, which could remove the singularities and satisfy a conformal invariance theory. A visualization of the evolution of the 4D relativistic branes over the conformal space-time of the 4D bulk is presented.

Supplementary and Associated Material

https://www.mdpi.com/2673-9984/2/1/61: Conference proceeding paper based on these findings

Keywords

Conformal Einstein Field Equations; Boundary Terms; Brane-World.

Subject

PHYSICAL SCIENCES, General & Theoretical Physics

Comments (1)

Comment 1
Received: 18 November 2021
Commenter: Mohammed Al-Fadhli
Commenter's Conflict of Interests: Author
Comment:
Dear Editor, 

I hope you are very well

This version includes developed mathematical derivations regarding the Lagrangian density variation on the boundary. It also includes a new figure to visualize the evolution of the 4D relativistic branes over the conformal space-time of the 4D bulk 

Kind regards,
Mohammed
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