Abstract
Parametric manifolds are reparametrisation-invariant geometric structures describing space-time and internal degrees of freedom in a unified framework. Using the theory of parametric spinors, a decomposition of the space-time in general relatively is developed with respect to the three-space of trajecories of a time-like vector field. The parametric 3+1 decomposition surpasses the ADM formalism in generality since it is possible even in space-times which do not admit a space-like foliation.
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