Unraveling gravity beyond Einstein with extended test bodies

TL;DR

This paper derives covariant equations of motion for test bodies in a broad class of gravitational theories with nonminimal matter coupling, extending classic results and enabling future tests of alternative gravity models.

Contribution

It generalizes the Mathisson-Papapetrou-Dixon equations to a wide range of non-Einsteinian theories with nonminimal coupling, providing a foundational framework for testing gravity.

Findings

Equations of motion for structureless test bodies are surprisingly simple.

The derived equations are applicable to a large class of gravitational theories.

The work sets the stage for systematic experimental tests of alternative gravity theories.

Abstract

The motion of test bodies in gravity is tightly linked to the conservation laws. This well-known fact in the context of General Relativity is also valid for gravitational theories which go beyond Einstein's theory. Here we derive the equations of motion for test bodies for a very large class of gravitational theories with a general nonminimal coupling to matter. These equations form the basis for future systematic tests of alternative gravity theories. Our treatment is covariant and generalizes the classic Mathisson-Papapetrou-Dixon result for spinning (extended) test bodies. The equations of motion for structureless test bodies turn out to be surprisingly simple, despite the very general nature of the theories considered.