The static spherically symmetric interior case of the non-symmetric theory of gravitation

Abstract

The field equations for a spherically symmetric perfect fluid in non-symmetric gravitational theory are cast as a set of first-order differential equations suitable for numerical integration. An analytic series solution is presented as an expansion around r=0. It is shows how interior solutions match with the exterior one and how, at the boundary, the Euler equation for the fluid becomes the equation of motion of a test particle in the exterior metric. An expression is derived from a conserved pseudotensor for the total mass-energy of a static body in terms of its interior matter parameters.

Interior problem in a ponsymmetric theory of gravitation

“…The approach is similar to the one studied by Savaria [4] in the context of a different nonsymmetric theory. The equations are put into a form of four first-order differential equations which are ready for numerical integration.…”

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

“…(This can be seen directly from the block-diagonal form of the GR metric). The first set explicitly involves the three skew functions g [01] , g [02] , g [12] : √ −gg [µν] ,ν…”

“…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.…”

Spherical collapse of a nonrotating perfect fluid in the non-symmetric theory of gravitation

“…The theory also rests on a Lagrangian density which, in terms of the a priori unconstrained.connection M ' : , , takes the unique form (Savaria 1989):…”

“…. In strict analogy with the static problem (Savaria 1989), this is the NGT charge contained within a sphere labelled by T at time 2. Now, in order to keep the expanded field equations (2.40) as compact as possible, we propose to use the following quantities similar to the ones which were helpful i n our study of the static case:…”