N-dimensional geometries and Einstein equations from systems of PDE's

Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology

Scientific paper

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Scientific paper

10.1142/S021827180701119X

The aim of the present work is twofold: first, we show how all the
$n$-dimensional Riemannian and Lorentzian metrics can be constructed from a
certain class of systems of second-order PDE's which are in duality to the
Hamilton-Jacobi equation and second we impose the Einstein equations to these
PDE's.

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