Cosmological solution of Bianchi type I in a new theory of gravitation

Abstract

%e present a homogeneous, plane-symmetric, matter-free solution to a new theory of gravitation. In the limit of large t, the solution goes over into the plane-symmetric Kasner metric of general relativity,

On the (im)possibility of a supersymmetric extension of NGT

“…Had one chosen ordinary complex numbers, then one would have ended up with U(3, 1, C) which is not isomorphic to GL(4, R). The group U(3, 1, H ) plays the same role in NGT as does the local homogeneous Lorentz group SO (3,1) in general relativity.…”

“…In contrast, the nonsymmetric metric g µν fully describes gravitation in NGT. A considerable amount of work has been devoted to the investigation of the phenomenological consequences of this theory [3], as well as to its geometrical interpretation [4,5,6]. The early version of this theory describes, in the linear approximation [7], the propagation of a massless spin 2 graviton and a scalar particle, the so called skewon, which would be the exchange particle of a long range fifth force, in addition to the gravitational one.…”

Cosmological solution with matter in a new theory of gravitation

“…detail the particular solutions for dust-filled and A series of papers has laid the foundations of radiation-dominated universes, we find that at the a new theory of gravitation and explored some of beginning of the expanding phase of the universe, the its consequences (2,3).…”

“…Basic Formalism: Field Equations, Conservation plane-symmetric non-static solution in the Dresence Laws, and Stress-energy Tensor of the energy-momentum tensor of a perfect fluid A contravariant non-symmetric tensor g p v can be written in comoving coordinates. Exploring in some obtained from the covariant tensor gpv by the relation In addition to r,," we introduce for convenience another non-symmetric affine connection, WpvA, obtained from T, , " through the projective transformation : [2.3] w, ; = r,; --~6 3 &I A Wv where [2.4] W, = +(W,," -W,,") It follows from [2.3] that study, we must write the most general g,, describing a homogeneous, plane-symmetric, non-static (Bianchi type I) space-time in comoving coordinates (3) In the cartesian coordinates we have adopted, the universe is open in the x 2 -x 3 plane of symmetry. The line element corresponding to the tensor [2.16] is given by The components of T,, can now be written explicitly in terms of p, p, and the components of g,,:…”

Gravitational waves from an axi-symmetric source in the Nonsymmetric Gravitational Theory

“…Since NGT was introduced [10] there have been few analytic solutions of the field equations published. The exact solutions known to date include the spherically symmetric vacuum case [11], the spherically symmetric interior case [12,13] and Bianchi type I cosmological solutions with and without matter [14,15]. This, at least in part, follows from the fact that deriving NGT field equations relevant for particular cases of interest is not as technically simple as may be suggested by its superficial similarity to the corresponding GR situations.…”