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EinsteinHamilton
In the Hamiltonian formulation of general relativity, the Einstein-Hamilton equations are:
The Hamiltonian
The lapse function is a scalar field that measures the rate at which coordinate time advances relative to proper time along a timelike trajectory in the manifold. Mathematically, if
The shift vector is a vector field on the spatial slice that represents the rate at which the spatial coordinates of an observer change as they move from one spatial slice to a neighboring one in the foliation. Formally, if
A spatial slice is a three-dimensional, spacelike hypersurface