The physical foundations for the geometric structure of relativistic theories of gravitation. From General Relativity to Extended Theories of Gravity through Ehlers-Pirani-Schild approach

TL;DR

This paper critically examines the physical foundations of the geometric structure in relativistic gravity theories using the Ehlers-Pirani-Schild formalism, clarifying how observables relate to both General Relativity and extended theories like f(R) gravity.

Contribution

It demonstrates how the Ehlers-Pirani-Schild approach disentangles geodesic and causal structures, enabling accurate analysis of observations in various gravity theories.

Findings

The formalism clarifies the relationship between observables and geometric structures.

It shows the applicability of the approach to extended theories like f(R) gravity.

Disentangling geodesic and causal structures improves observational analysis.

Abstract

We discuss in a critical way the physical foundations of geometric structure of relativistic theories of gravity by the so-called Ehlers-Pirani-Schild formalism. This approach provides a natural interpretation of the observables showing how relate them to General Relativity and to a large class of Extended Theories of Gravity. In particular we show that, in such a formalism, geodesic and causal structures of space-time can be safely disentangled allowing a correct analysis in view of observations and experiment. As specific case, we take into account the case of f(R) gravity.