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

Universe

Øyvind G. Grøn¹  Matthew T. Aadne² 

[1] Oslo and Akershus University College of Applied Sciences, Faculty of Technology, Art and Sciences, PB 4 St. Olavs. Pl., NO-0130 Oslo, Norway;University of Stavanger, P.O. Box 8600 Forus, 4036 Stavanger, Norway;

关键词: Nash;    theory of gravity;    solutions;   

DOI  :  10.3390/universe3010010

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown