Institute of Theoretical Physics · Faculty of Mathematics and Physics, Charles University
Phys. Rev. D 111(6), 064062 (2025)
We analyze all possible symmetry reductions of Lagrangians that yield fully equivalent field equations
for any 4-dimensional metric theory of gravity. Specifically, we present a complete list of infinitesimal
group actions obeying the principle of symmetric criticality, identify the corresponding invariant metrics
(and l-chains), discuss relations among them, and analyze simplifications allowed by the residual
diffeomorphism group and Noether identities before and after variation of the reduced Lagrangian. We
employ rigorous treatment of the symmetry reduction by Fels and Torre and use the Hicks classification of
infinitesimal group actions by means of Lie algebras pairs of isometries and their isotropy subalgebras. The
classification is recast in the coordinates in which the well-known symmetries and geometries are easily
recognizable and relatable to each other. The paper is accompanied by a code for the symmetry reduction of
Lagrangians that we developed in xAct package of Mathematica.
@article{UTF1057,
author = {Frausto, G. and Kolář, I. and Málek, T. and Torre, Ch.},
title = {{Symmetry reduction of gravitational Lagrangians}},
journal = {Phys. Rev. D},
volume = {111},
number = {6},
pages = {064062},
year = {2025},
month = {3},
doi = {10.1103/PhysRevD.111.064062},
eprint = {2410.11036},
archivePrefix = {arXiv},
url = {https://doi.org/10.1103/PhysRevD.111.064062},
}