Energy nonconservation and relativistic trajectories: Unimodular gravity and beyond

TL;DR

This paper explores how energy nonconservation can be incorporated into gravity theories, deriving particle trajectories under such conditions, with a focus on unimodular gravity and constraints from Solar system data.

Contribution

It identifies conditions for energy-momentum nonconservation, derives trajectories for energy-losing particles, and applies these concepts to unimodular gravity with observational limits.

Findings

Energy nonconservation induces specific accelerations in particle trajectories.

In unimodular gravity, trajectories can be analytically determined under spherical symmetry.

Solar system observations place bounds on energy nonconservation parameters.

Abstract

Energy conservation has the status of a fundamental physical principle. However, measurements in quantum mechanics do not comply with energy conservation. Therefore, it is expected that a more fundamental theory of gravity -- one that is less incompatible with quantum mechanics -- should admit energy nonconservations. This paper begins by identifying the conditions for a theory to have an energy-momentum tensor that is not conserved. Then, the trajectory equation for pointlike particles that lose energy is derived, showing that energy nonconservation produces a particular acceleration. As an example, the unimodular theory of gravity is studied. Interestingly, in spherical symmetry, given that there is a generalized Birkhoff theorem and that the energy-momentum tensor divergence is a closed form, the trajectories of test particles that lose energy can be found using well known methods. Finally, limits on the energy nonconservation parameters are set using Solar system observations.