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In this paper we show how a gravitational field generated by a givenenergy-momentum distribution (for all realistic cases) can be represented bydistinct geometrical structures (Lorentzian, teleparallel and non nullnonmetricity spacetimes) or that we even can dispense all those geometricalstructures and simply represent the gravitational field as a field in theFaraday's sense living in Minkowski spacetime. The explicit Lagrangian densityfor this theory is given and the field equations (which are Maxwell's likeequations) are shown to be equivalent to Einstein's equations. Some examplesare worked in detail in order to convince the reader that the geometricalstructure of a manifold (modulus some topological constraints) is conventionalas already emphasized by Poincare long ago, and thus the realization that thereare disctints geometrical representations (and a physical model related to adeformation of the continuum supporting Minkowski spacetime) for any realisticgravitational field strongly suggests that we must investigate the origin ofits physical nature. We hope that this paper will convince readers that this isindeed the case.

Some Thoughts on Geometries and on the Nature of the Gravitational Field