Is General Relativity a simpler theory?

TL;DR

This paper argues that gravity, like other interactions, should be understood as a modification of a higher-dimensional Finsler space rather than just spacetime, challenging the simplicity of General Relativity's geometric approach.

Contribution

It introduces the idea that gravity's geometric description involves a Finsler metric space with additional dimensions, extending the variational formalism beyond spacetime.

Findings

Gravity modifies Finsler metrics in higher-dimensional space.

Spinning particles require a richer geometric framework than spinless particles.

Simplifying gravity to spacetime metric modifications overlooks the full geometric complexity.

Abstract

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 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 an elementary particle is greater than spacetime. This manifold for any mechanical system is a Finsler metric space such that the variational formalism can always be interpreted as a geodesic problem on this 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 spacetime metric is to make a simpler theory, the gravitational theory of spinless matter. Even the usual assumption that the modification of the metric only involves dependence of the metric coefficients on the spacetime variables is also a restriction because in general these coefficients are dependent on the velocities. In the spirit of unification of all forces, gravity cannot produce, in principle, a different and simpler geometrization than any other interaction.