Modified geodesic equations of motion for compact bodies in alternative theories gravity

TL;DR

This paper derives exact modified geodesic equations for self-gravitating bodies in alternative gravity theories, generalizing general relativity and enabling high-precision motion analysis.

Contribution

It introduces a theory-independent formulation of equations of motion for compact bodies accounting for variable masses due to alternative gravity fields.

Findings

Equations reduce to GR geodesics when masses are constant.

Provides a framework for high-order post-Newtonian calculations.

Applicable to a broad class of alternative gravity theories.

Abstract

We derive exact, modified geodesic equations for a system of non-spinning, self-gravitating interacting bodies in a class of alternative theories of gravity to general relativity. We use a prescription proposed by Eardley for incorporating the effects of self-gravity within gravitationally bound bodies, in which their masses may depend on invariant quantities constructed from the auxiliary scalar, vector or tensor fields introduced by such theories, evaluated in the vicinity of each body. The forms of the equations are independent of the field equations of the chosen theory. In the case where the masses are strictly constant, the equations reduce to the conventional geodesic equations of general relativity. These equations may be useful tools for deriving equations of motion for compact bodies to high post-Newtonian orders in alternative theories of gravity.