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arXiv · 2211.06532

Energy nonconservation and relativistic trajectories: Unimodular gravity and beyond

Y. Bonder·J. E. Herrera·A. M. Rubiol
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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.

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Y. Bonder, J. E. Herrera, A. M. Rubiol. 2022-11-12. Energy nonconservation and relativistic trajectories: Unimodular gravity and beyond. https://doi.org/10.1103/physrevd.107.084032

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