The Equivalence Principle is NOT a Noether Symmetry

Abstract

The connection between the Equivalence Principle and Noether's theorem was discussed in S. Capozziello and C. Ferrara, Int. J. Geom. Meth. Mod. Phys. 21, 2440014 (2024). However, it is known that the Noether symmetry condition is independent of the equations of motions as follows from Hamilton's Principle. In this paper, we critically examine the analysis presented in the aforementioned work, highlighting its flaws, and provide a detailed demonstration that there is no connection between Noether's theorem and the Equivalence Principle. Furthermore, we offer various insights on symmetry analysis to prevent the perpetuation of inaccuracies regarding Noether's work.

8 pages, no figures, published in Eur. Phys. J. C

References in corpus (3)

• Projective collineations of decomposable spacetimes generated by the Lie point symmetries of geodesic equations
• The Equivalence Principle as a Noether Symmetry
• Cubic first integrals of autonomous dynamical systems in $E^2$ by an algorithmic approach