N-dimensional geometries and Einstein equations from systems of PDE's
Emanuel Gallo, Magdalena Marciano-Melchor, Gilberto Silva-Ortigoza
Abstract
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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