{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:50:13Z","timestamp":1760233813668,"version":"build-2065373602"},"reference-count":53,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,2,20]],"date-time":"2021-02-20T00:00:00Z","timestamp":1613779200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Consejo Nacional de Ciencia y Tecnolog\u00eda (CONACYT), M\u00e9xico","award":["A1-S-7701"],"award-info":[{"award-number":["A1-S-7701"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We report off-shell Noether currents obtained from off-shell Noether potentials for first-order general relativity described by n-dimensional Palatini and Holst Lagrangians including the cosmological constant. These off-shell currents and potentials are achieved by using the corresponding Lagrangian and the off-shell Noether identities satisfied by diffeomorphisms generated by arbitrary vector fields, local SO(n) or SO(n\u22121,1) transformations, \u2018improved diffeomorphisms\u2019, and the \u2018generalization of local translations\u2019 of the orthonormal frame and the connection. A remarkable aspect of our approach is that we do not use Noether\u2019s theorem in its direct form. By construction, the currents are off-shell conserved and lead naturally to the definition of off-shell Noether charges. We also study what we call the \u2018half off-shell\u2019 case for both Palatini and Holst Lagrangians. In particular, we find that the resulting diffeomorphism and local SO(3,1) or SO(4) off-shell Noether currents and potentials for the Holst Lagrangian generically depend on the Immirzi parameter, which holds even in the \u2018half off-shell\u2019 and on-shell cases. We also study Killing vector fields in the \u2018half off-shell\u2019 and on-shell cases. The current theoretical framework is illustrated for the \u2018half off-shell\u2019 case in static spherically symmetric and Friedmann\u2013Lemaitre\u2013Robertson\u2013Walker spacetimes in four dimensions.<\/jats:p>","DOI":"10.3390\/sym13020348","type":"journal-article","created":{"date-parts":[[2021,2,21]],"date-time":"2021-02-21T21:15:01Z","timestamp":1613942101000},"page":"348","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Off-Shell Noether Currents and Potentials for First-Order General Relativity"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4936-9170","authenticated-orcid":false,"given":"Merced","family":"Montesinos","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica, Cinvestav, Avenida Instituto Polit\u00e9cnico Nacional 2508, San Pedro Zacatenco, 07360 Gustavo A. Madero, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0206-7378","authenticated-orcid":false,"given":"Diego","family":"Gonzalez","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Cinvestav, Avenida Instituto Polit\u00e9cnico Nacional 2508, San Pedro Zacatenco, 07360 Gustavo A. Madero, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5529-6991","authenticated-orcid":false,"given":"Rodrigo","family":"Romero","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Cinvestav, Avenida Instituto Polit\u00e9cnico Nacional 2508, San Pedro Zacatenco, 07360 Gustavo A. Madero, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3519-4736","authenticated-orcid":false,"given":"Mariano","family":"Celada","sequence":"additional","affiliation":[{"name":"Centro de Ciencias Matem\u00e1ticas, Universidad Nacional Aut\u00f3noma de M\u00e9xico, UNAM-Campus Morelia, Apartado Postal 61-3, Morelia, 58090 Michoac\u00e1n, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,20]]},"reference":[{"key":"ref_1","first-page":"235","article-title":"Invariante Variations probleme","volume":"1918","author":"Noether","year":"1918","journal-title":"Nachr. K\u00f6nig. Ges. Wiss. G\u00f6ttingen Math-Phys. Kl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1007\/BF01459410","article-title":"\u00dcber die Erhaltungss\u00e4tze der Elektrodynamik","volume":"84","year":"1921","journal-title":"Math. 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