@misc{10481/62663,
year = {2020},
month = {4},
url = {http://hdl.handle.net/10481/62663},
abstract = {Physical foundations for relativistic spacetimes are revisited in order to check at what
extent Finsler spacetimes lie in their framework. Arguments based on inertial observers (as in the
foundations of special relativity and classical mechanics) are shown to correspond with a double
linear approximation in the measurement of space and time. While general relativity appears
by dropping the first linearization, Finsler spacetimes appear by dropping the second one. The
classical Ehlers–Pirani–Schild approach is carefully discussed and shown to be compatible with the
Lorentz–Finsler case. The precise mathematical definition of Finsler spacetime is discussed by using
the space of observers. Special care is taken in some issues such as the fact that a Lorentz–Finsler
metric would be physically measurable only on the causal directions for a cone structure, the
implications for models of spacetimes of some apparently innocuous hypotheses on differentiability,
or the possibilities of measurement of a varying speed of light.},
organization = {M.A.J. was partially supported by MICINN/FEDER project reference PGC2018- 097046-B-I00
and Fundación Séneca project reference 19901/GERM/15, Spain, and M.S. was supported by Spanish
MINECO/FEDER project reference MTM2016-78807-C2-1-P. This work is included in the framework of the
Programme of Excellence Groups of the Region of Murcia, Spain funded by Fundación Séneca, Science, and
Technology Agency of the Region of Murcia.},
publisher = {MDPI},
keywords = {Finsler spacetime},
keywords = {Ehlers–Pirani–Schild approach},
keywords = {Lorentz symmetry breaking},
keywords = {Very special relativity},
keywords = {Signature-changing spacetimes},
title = {Foundations of Finsler Spacetimes from the Observers’ Viewpoint},
doi = {10.3390/universe6040055},
author = {Sánchez Caja, Miguel and Bernal, Antonio N.},
}