Preserved in Portico This version is not peer-reviewed
Derivation of a Generalized Einstein's Equation of Gravitation Based on a Mechanical Model of Vacuum and a Sink Flow Model of Particles
: Received: 19 June 2018 / Approved: 22 June 2018 / Online: 22 June 2018 (06:19:33 CEST)
: Received: 28 August 2018 / Approved: 30 August 2018 / Online: 30 August 2018 (06:20:25 CEST)
: Received: 23 January 2019 / Approved: 24 January 2019 / Online: 24 January 2019 (09:05:28 CET)
: Received: 6 October 2019 / Approved: 8 October 2019 / Online: 8 October 2019 (07:07:19 CEST)
: Received: 14 October 2019 / Approved: 15 October 2019 / Online: 15 October 2019 (08:07:59 CEST)
: Received: 29 October 2019 / Approved: 29 October 2019 / Online: 29 October 2019 (16:00:57 CET)
: 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
There exist some puzzles and difficulties related to Einstein's theory of general relativity. We generalize our previous theory of gravitation by methods of special relativistic continuum mechanics. In inertial coordinate systems, 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. A generalized Einstein's equation is derived in inertial coordinate systems based on some assumptions. This equation reduces to Einstein's equation in case of weak field in harmonic coordinate systems. In some special non-inertial coordinate systems, a second generalized Einstein's equation is derived based on some assumptions. If the field is weak and the coordinate system is quasi-inertial and harmonic, the second generalized Einstein's equation reduces to Einstein's equation. There exists some differences between this theory and Einstein's theory of general relativity.
Einstein's equation; gravitation; general relativity; sink; gravitational aether
PHYSICAL SCIENCES, General & Theoretical Physics
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