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Keywords = FLRW space-times, static spherically-symmetric space-times

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7 pages, 230 KiB  
Article
Exact Solutions of the Field Equations for Empty Space in the Nash Gravitational Theory
by Matthew T. Aadne and Øyvind G. Grøn
Universe 2017, 3(1), 10; https://doi.org/10.3390/universe3010010 - 14 Feb 2017
Cited by 6 | Viewed by 4993
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 [...] Read more.
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. Full article
20 pages, 281 KiB  
Article
Modified Gravity Models Admitting Second Order Equations of Motion
by Aimeric Colléaux and Sergio Zerbini
Entropy 2015, 17(10), 6643-6662; https://doi.org/10.3390/e17106643 - 25 Sep 2015
Cited by 3 | Viewed by 4535
Abstract
The aim of this paper is to find higher order geometrical corrections to the Einstein–Hilbert action that can lead only to second order equations of motion. The metric formalism is used, and static spherically-symmetric and Friedmann–Lemaître space-times are considered, in four dimensions. The [...] Read more.
The aim of this paper is to find higher order geometrical corrections to the Einstein–Hilbert action that can lead only to second order equations of motion. The metric formalism is used, and static spherically-symmetric and Friedmann–Lemaître space-times are considered, in four dimensions. The Fulling, King, Wybourne and Cummings (FKWC) basis is introduced in order to consider all of the possible invariant scalars, and both polynomial and non-polynomial gravities are investigated. Full article
(This article belongs to the Special Issue Entropy in Quantum Gravity and Quantum Cosmology)
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