Hypersurface orthogonal decomposition and analysis of the skew sector of a massive nonsymmetric gravitational theory linearized on a curved background
Abstract
Although General Relativity still provides the best classical description
of gravitational phenomenon it leads to the following unfortunate
predictions about the Universe :-
(i) that there was a singularity in the beginning of the universe i.e
the big-bang singulari ty
(ii)that there is a singularity in the gravitational collapse scenario.
These predictions mean that the theory is invalidated as the singularity
cannot be probed, a situation which leads to information loss. Thus
because of this failure of General Relativity, a need arose to look for an
alternative theory which would circumvent this information loss. This alternative
came in the name of Nonsymmetric Gravitational Theory (NGT)
as a proposal by J.W.Moffat in 1979 [10]. In NGT the singularities can be
avoided because it predicts a superdense object instead of a blackhole and
so no information loss is anticipated [15]. However, the original versions
of NGT were found to be confronted with consistency problems due to the
absence of a massless gauge invariance in the skew sector of the theory.
Consequently it was shown in the works of Damour ,Desser and McCarthy
[18,19] that the problem could be avoided by considering a theory which
mimmicks a massive Proca-type model which does not require such gauge
mvariance.
In the spirit of this line of thought NGT was extended to a massive
NGT [35] which in the linear approximation reduces to a massive Kalb-
Ramond f.eld. The Proca-like massive antisymmetric gauge field does not
require a gauge invariance for well-behaved positive energy solutions. It
is this massive NGT , linearized on a curved background, which has been
considered in this work, more specifically the skew sector of it. The dynamics
of the theory have been investigated by performing a 3+1 foliation
of spacetime, leading to constraint and evolution equations. These two
sets of equations have been shown to be consistent and possibly devoid
of linearization instabilty. The resulting field equations, because of their
consistency, are suitable for numerical relativity and can also serve as a
starting point for canonical quantization of gravity.
Citation
Degree of Doctor of Philosophy,Sponsorhip
University of NairobiPublisher
Department of Physics, University of Nairobi,