Energy nonconservation and relativistic trajectories: Unimodular gravity and beyond

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 more theory gravity -- one less incompatible should admit nonconservations. This paper begins by identifying conditions for to have an energy-momentum tensor conserved. Then, trajectory equation pointlike particles lose derived, showing nonconservation produces particular acceleration. As example, unimodular studied. Interestingly, spherical symmetry, given there generalized Birkhoff theorem and divergence closed form, trajectories test can be found using well known methods. Finally, limits on parameters are set Solar system observations.