On the Significance of the Stress–Energy Tensor in Finsler Spacetimes Javaloyes, Miguel Ángel Sánchez Caja, Miguel Fernández Villaseñor, Fidel Divergence in Finsler manifolds Stress–energy tensor Finsler spacetime Lorentz symmetry breaking Very special relativity MAJ was partially supported by the project PGC2018-097046-B-I00 funded by MCIN/ AEI /10.13039/501100011033/ FEDER “Una manera de hacer Europa” and Fundación Séneca project with reference 19901/GERM/15. This work is a result of the activity developed within the framework of the Programme in Support of Excellence Groups of the Región de Murcia, Spain, by Fundación Séneca, Science and Technology Agency of the Región de Murcia. MS and FFV were partially supported by the project PID2020-116126GB-I00 funded by MCIN/AEI/10.13039/501100011033, by the project PY20-01391 (PAIDI 2020) funded by Junta de Andalucía—FEDER and by the framework of IMAG-María de Maeztu grant CEX2020-001105-M funded by MCIN/AEI/10.13039/50110001103. We revisit the physical arguments that led to the definition of the stress–energy tensor T in the Lorentz–Finsler setting (M, L) starting with classical relativity. Both the standard heuristic approach using fluids and the Lagrangian one are taken into account. In particular, we argue that the Finslerian breaking of Lorentz symmetry makes T an anisotropic 2-tensor (i.e., a tensor for each L-timelike direction), in contrast with the energy-momentum vectors defined on M. Such a tensor is compared with different ones obtained by using a Lagrangian approach. The notion of divergence is revised from a geometric viewpoint, and, then, the conservation laws of T for each observer field are revisited. We introduce a natural anisotropic Lie bracket derivation, which leads to a divergence obtained from the volume element and the non-linear connection associated with L alone. The computation of this divergence selects the Chern anisotropic connection, thus giving a geometric interpretation to previous choices in the literature. 2022-02-16T12:55:13Z 2022-02-16T12:55:13Z 2022-01-31 journal article Javaloyes, M.A.; Sánchez, M.; Villaseñor, F.F. On the Significance of the Stress–Energy Tensor in Finsler Spacetimes. Universe 2022, 8, 93. [https://doi.org/10.3390/universe8020093] http://hdl.handle.net/10481/72874 10.3390/universe8020093 eng http://creativecommons.org/licenses/by/3.0/es/ open access Atribución 3.0 España MDPI