Spacelike Foliations Research Articles

The parametric manifold picture of space-time

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.

Group-theoretic approach to the construction of relativistic lagrangian mechanics of a system of particles

Mathematical aspects of the Lagrangian formalism of relativistic mechanics of a system of interacting particles are considered. A geometric definition of a form of relativistic dynamics possessing the spacelike or isotropic foliation of Minkowski space is introduced. A realization of the Lie algebra of the Poincare group by means of Lie-Backlund vector fields on a general jet continuation of the configuration space is constructed. Invariance conditions of Lagrangian relativistic mechanics are formulated and investigated; the characteristic features of this formalism, which arises as a consequence of the demands of Poincare invariance, are described.

Null surface geometrodynamics

Investigates the dynamical structure of Einstein's theory of gravity using a time parameter whose level surfaces are null hypersurfaces in spacetime. A spacelike foliation of codimension two is used in order to give an invariant kinematic description. Dynamics are analysed via a constrained Hamiltonian formalism. It is found that the Hamiltonian formulation includes both first and second class constraints. The first class constraints are associated with the invariance of the theory with respect to diffeomorphisms of the null hypersurfaces. The second class constraints are direct consequences of the choice of null time parameter.

Spacelike foliations by $(n - 1)$-umbilical hypersurfaces in spacetimes

Spacelike foliations by $(n - 1)$-umbilical hypersurfaces in spacetimes