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

Gallo, Emanuel; Marciano-Melchor, Magdalena; Silva-Ortigoza, Gilberto

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

Authors

Gallo, Emanuel

Marciano-Melchor, Magdalena

Silva-Ortigoza, Gilberto

Description

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.