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.