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Universe 2017, 3(1), 10; doi:10.3390/universe3010010

Exact Solutions of the Field Equations for Empty Space in the Nash Gravitational Theory

1
University of Stavanger, P.O. Box 8600 Forus, 4036 Stavanger, Norway
2
Oslo and Akershus University College of Applied Sciences, Faculty of Technology, Art and Sciences, PB 4 St. Olavs. Pl., NO-0130 Oslo, Norway
*
Author to whom correspondence should be addressed.
Academic Editor: Lorenzo Iorio
Received: 17 December 2016 / Revised: 4 February 2017 / Accepted: 7 February 2017 / Published: 14 February 2017
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Abstract

John Nash has proposed a new theory of gravity. We define a Nash-tensor equal to the curvature tensor appearing in the Nash field equations for empty space, and calculate its components for two cases: 1. A static, spherically symmetric space; and 2. The expanding, homogeneous and isotropic space of the Friedmann-Lemaitre-Robertson-Walker (FLRW) universe models. We find the general, exact solution of Nash’s field equations for empty space in the static case. The line element turns out to represent the Schwarzschild-de Sitter spacetime. Also we find the simplest non-trivial solution of the field equations in the cosmological case, which gives the scale factor corresponding to the de Sitter spacetime. Hence empty space in the Nash theory corresponds to a space with Lorentz Invariant Vacuum Energy (LIVE) in the Einstein theory. This suggests that dark energy may be superfluous according to the Nash theory. We also consider a radiation filled universe model in an effort to find out how energy and matter may be incorporated into the Nash theory. A tentative interpretation of the Nash theory as a unified theory of gravity and electromagnetism leads to a very simple form of the field equations in the presence of matter. It should be noted, however, that the Nash theory is still unfinished. A satisfying way of including energy momentum into the theory has yet to be found. View Full-Text
Keywords: Nash; theory of gravity; solutions Nash; theory of gravity; solutions
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. (CC BY 4.0).

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Aadne, M.T.; Grøn, Ø.G. Exact Solutions of the Field Equations for Empty Space in the Nash Gravitational Theory. Universe 2017, 3, 10.

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