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On the relation between the canonical Hamilton-Jacobi equation and the De Donder-Weyl Hamilton-Jacobi formulation in general relativity
Published 31 Dec 2019 in gr-qc | (1912.13363v1)
Abstract: We discuss the relation between the canonical Hamilton-Jacobi theory and the De Donder-Weyl Hamilton-Jacobi theory known in the calculus of variations using the examples of a scalar field in curved space-time and general relativity. By restricting ourselves to the Gaussian coordinates we show how the canonical Hamilton-Jacobi equation of general relativity can be derived from the De Donder-Weyl Hamilton-Jacobi formulation of the Einstein equations.
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