Preprint Article Version 7 Preserved in Portico This version is not peer-reviewed

# Derivation of Generalized Einstein's Equations of Gravitation in Inertial Systems Based on a Sink Flow Model of Particles

Version 1 : Received: 19 June 2018 / Approved: 22 June 2018 / Online: 22 June 2018 (06:19:33 CEST)
Version 2 : Received: 28 August 2018 / Approved: 30 August 2018 / Online: 30 August 2018 (06:20:25 CEST)
Version 3 : Received: 23 January 2019 / Approved: 24 January 2019 / Online: 24 January 2019 (09:05:28 CET)
Version 4 : Received: 6 October 2019 / Approved: 8 October 2019 / Online: 8 October 2019 (07:07:19 CEST)
Version 5 : Received: 14 October 2019 / Approved: 15 October 2019 / Online: 15 October 2019 (08:07:59 CEST)
Version 6 : Received: 29 October 2019 / Approved: 29 October 2019 / Online: 29 October 2019 (16:00:57 CET)
Version 7 : Received: 18 February 2021 / Approved: 3 March 2021 / Online: 3 March 2021 (10:21:22 CET)

A peer-reviewed article of this Preprint also exists.

Journal reference: Reports on Mathematical Physics 2019
DOI: 10.1016/S0034-4877(19)30067-9

## Abstract

J. C. Maxwell, B. Riemann and H. Poincar$\acute{e}$ have proposed the idea that all microscopic particles are sink flows in a fluidic aether. Following this research program, a previous theory of gravitation based on a mechanical model of vacuum and a sink flow model of particles is generalized by methods of special relativistic continuum mechanics. In inertial reference frames, we construct a tensorial potential which satisfies the wave equation. Inspired by the equation of motion of a test particle, a definition of a metric tensor of a Riemannian spacetime is introduced. Applying Fock's theorem, generalized Einstein's equations in inertial systems are derived based on some assumptions. These equations reduce to Einstein's equations in case of weak field in harmonic reference frames. There exist some differences between this theory and Einstein's theory of general relativity.

## Keywords

Einstein's equations; gravitation; general relativity; sink; gravitational aether.

## Subject

PHYSICAL SCIENCES, Acoustics

Comment 1
Received: 3 March 2021
Commenter: Xiao-Song Wang
Commenter's Conflict of Interests: Author
Comment: The sections related to generalized Einstein's equations of gravitation in non-inertial systems are deleted.
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