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

Emanuel Gallo·Magdalena Marciano-Melchor·Gilberto Silva-Ortigoza
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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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Emanuel Gallo, Magdalena Marciano-Melchor, Gilberto Silva-Ortigoza. 2005-02-24. N-dimensional geometries and Einstein equations from systems of PDE's. https://doi.org/10.1142/s021827180701119x

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