Riemannian and non-Riemannian extensions of geometrodynamics versus Einsteinian gravity

TL;DR

This paper explores extensions of General Relativity, focusing on modified gravity theories, their Newtonian limits, and the behavior of autoparallel trajectories in generalized asymmetric metrics.

Contribution

It introduces new analyses of modified gravity models, their Newtonian limits, and the properties of autoparallel trajectories in asymmetric metrics.

Findings

Newtonian limit derived for a class of modified gravity actions

Autoparallel trajectories defined in generalized asymmetric metrics

Insights into extensions of Einsteinian gravity

Abstract

We analyze some extensions of General Relativity. Within the framework of modified gravity, the Newtonian limit of a class of gravitational actions is discussed on the basis of the corresponding scalar-tensor model. For a generalized asymmetric metric, autoparallel trajectories are defined under suitable conditions at first approximation order.