Unified formalism for Palatini gravity

Autores
Capriotti, Santiago
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This paper is devoted to the construction of a unified formalism for Palatini and unimodular gravity. The idea is to employ a relationship between unified formalism for a Griffiths variational problem and its classical Lepage-equivalent variational problem. The main geometrical tools involved in these constructions are canonical forms living on the first jet of the frame bundle for the spacetime manifold. These forms play an essential role in providing a global version of the Palatini Lagrangian and expressing the metricity condition in an invariant form. With them, we were able to find the associated equations of motion in invariant terms and, by using previous results from the literature, to prove their involutivity. As a bonus, we showed how this construction can be used to provide a unified formalism for the so-called unimodular gravity by employing a reduction of the structure group of the frame bundle to the special linear group.
Fil: Capriotti, Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Materia
VARIATIONAL PROBLEMS
UNIFIED FORMALISM
PALATINI GRAVITY
UNIMODULAR GRAVITY
CONNECTION BUNDLE
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/43072
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/43072
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Unified formalism for Palatini gravityCapriotti, SantiagoVARIATIONAL PROBLEMSUNIFIED FORMALISMPALATINI GRAVITYUNIMODULAR GRAVITYCONNECTION BUNDLEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This paper is devoted to the construction of a unified formalism for Palatini and unimodular gravity. The idea is to employ a relationship between unified formalism for a Griffiths variational problem and its classical Lepage-equivalent variational problem. The main geometrical tools involved in these constructions are canonical forms living on the first jet of the frame bundle for the spacetime manifold. These forms play an essential role in providing a global version of the Palatini Lagrangian and expressing the metricity condition in an invariant form. With them, we were able to find the associated equations of motion in invariant terms and, by using previous results from the literature, to prove their involutivity. As a bonus, we showed how this construction can be used to provide a unified formalism for the so-called unimodular gravity by employing a reduction of the structure group of the frame bundle to the special linear group.Fil: Capriotti, Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaWorld Scientific2017-12-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/43072Capriotti, Santiago; Unified formalism for Palatini gravity; World Scientific; International Journal of Geometric Methods in Modern Physics; 15; 3; 12-12-2017; 1-330219-88781793-6977CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.worldscientific.com/doi/abs/10.1142/S0219887818500445info:eu-repo/semantics/altIdentifier/doi/10.1142/S0219887818500445info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:53:51Zoai:ri.conicet.gov.ar:11336/43072instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:53:51.473CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Unified formalism for Palatini gravity
title Unified formalism for Palatini gravity
spellingShingle Unified formalism for Palatini gravity
Capriotti, Santiago
VARIATIONAL PROBLEMS
UNIFIED FORMALISM
PALATINI GRAVITY
UNIMODULAR GRAVITY
CONNECTION BUNDLE
title_short Unified formalism for Palatini gravity
title_full Unified formalism for Palatini gravity
title_fullStr Unified formalism for Palatini gravity
title_full_unstemmed Unified formalism for Palatini gravity
title_sort Unified formalism for Palatini gravity
dc.creator.none.fl_str_mv Capriotti, Santiago
author Capriotti, Santiago
author_facet Capriotti, Santiago
author_role author
dc.subject.none.fl_str_mv VARIATIONAL PROBLEMS
UNIFIED FORMALISM
PALATINI GRAVITY
UNIMODULAR GRAVITY
CONNECTION BUNDLE
topic VARIATIONAL PROBLEMS
UNIFIED FORMALISM
PALATINI GRAVITY
UNIMODULAR GRAVITY
CONNECTION BUNDLE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This paper is devoted to the construction of a unified formalism for Palatini and unimodular gravity. The idea is to employ a relationship between unified formalism for a Griffiths variational problem and its classical Lepage-equivalent variational problem. The main geometrical tools involved in these constructions are canonical forms living on the first jet of the frame bundle for the spacetime manifold. These forms play an essential role in providing a global version of the Palatini Lagrangian and expressing the metricity condition in an invariant form. With them, we were able to find the associated equations of motion in invariant terms and, by using previous results from the literature, to prove their involutivity. As a bonus, we showed how this construction can be used to provide a unified formalism for the so-called unimodular gravity by employing a reduction of the structure group of the frame bundle to the special linear group.
Fil: Capriotti, Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina
description This paper is devoted to the construction of a unified formalism for Palatini and unimodular gravity. The idea is to employ a relationship between unified formalism for a Griffiths variational problem and its classical Lepage-equivalent variational problem. The main geometrical tools involved in these constructions are canonical forms living on the first jet of the frame bundle for the spacetime manifold. These forms play an essential role in providing a global version of the Palatini Lagrangian and expressing the metricity condition in an invariant form. With them, we were able to find the associated equations of motion in invariant terms and, by using previous results from the literature, to prove their involutivity. As a bonus, we showed how this construction can be used to provide a unified formalism for the so-called unimodular gravity by employing a reduction of the structure group of the frame bundle to the special linear group.
publishDate 2017
dc.date.none.fl_str_mv 2017-12-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/43072
Capriotti, Santiago; Unified formalism for Palatini gravity; World Scientific; International Journal of Geometric Methods in Modern Physics; 15; 3; 12-12-2017; 1-33
0219-8878
1793-6977
CONICET Digital
CONICET
url http://hdl.handle.net/11336/43072
identifier_str_mv Capriotti, Santiago; Unified formalism for Palatini gravity; World Scientific; International Journal of Geometric Methods in Modern Physics; 15; 3; 12-12-2017; 1-33
0219-8878
1793-6977
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.worldscientific.com/doi/abs/10.1142/S0219887818500445
info:eu-repo/semantics/altIdentifier/doi/10.1142/S0219887818500445
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv World Scientific
publisher.none.fl_str_mv World Scientific
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.069144

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