Authors: Anamitra Palit
The paper investigates the possibility of continuous variation of a manifold starting from a given one. Theoretical investigation engenders the fact that such a continuous passage is not possible provided you start from a given manifold specified by its metric coefficients. You have to move in discrete steps starting from the given one, satisfying some equations discussed in the paper. A manifold surface can always be constructed using arbitrary continuous and differentiable functions as metric coefficients. The ensuing Ricci tensor and Ricci scalar will always satisfy the Bianchi Identity and hence the field equations. The functionals in the general Relativity use the Ricci scalar [ensuing from the metric coefficients] as arguments. Different surfaces[manifolds ] are generated by varying the metric coefficients [in order to vary the Ricci scalar or such functions as dependent on it]. In each case the manifold satisfies the Bianchi identity and hence the Field Equations prior to the application of the stationary action principle. This perhaps induces a motivation for discretization. Discretization will modify all the principles involved in General Relativity making them of a suitable nature in the present context. This may open up the gates for including the General Relativity Lagrangians in a more rigorous manner.
Comments: 37 Pages.
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[v1] 2015-06-11 03:23:56
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