Abstract
Things should be made simple, but not simpler.
What we want to show is that General Relativity, as it stands today, can be considered as a gravitational theory of low velocity spinless matter, and therefore a restricted theory of gravitation.
Gravity is understood as a geometrization of spacetime. But spacetime is also the manifold of the boundary values of the spinless point particle in a variational approach. Since all known elementary matter, baryons, leptons and gauge bosons are spinning objects, it means that the manifold, which we call the kinematical space, where we play the game of the variational formalism of a classical elementary particle must be greater than spacetime.
Mathematics shows that this manifold for any arbitrary mechanical system is always a Finsler metric space, such that the variational formalism can be interpreted as a geodesic problem on this metric space.
This manifold is just the flat Minkowski space for the free spinless particle. Any interaction modifies its flat Finsler metric as gravitation does.
The same thing happens for the spinning objects, but now the Finsler metric space has more dimensions and its metric is modified by any interaction, so that to reduce gravity to the modification only of the metric of the spacetime submanifold is to make a simpler theory, the gravitational theory of spinless matter.
Even the usual assumption that the modification of the metric only produces a Riemannian metric of the spacetime is also a restriction because in general the coefficients for a Finsler metric, are also dependent on the velocities. Removal of the velocity dependence of metric coefficients is equivalent to consider the restriction to low velocity matter.
In the spirit of unification of all forces, gravity cannot produce, in principle, a different and simpler geometrization than any other interaction.
References: arXiv: 1203.4076
