On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes

Autores
Gamboa Saravi, Ricardo Enrique; Sanmartino, Marcela; Tchamitchian, Philippe
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We give simple conditions implying the well-posedness of the Cauchy problem for the propagation of classical scalar fields in general (n + 2)-dimensional static and spherically symmetric spacetimes. They are related to the properties of the underlying spatial part of the wave operator, one of which being the standard essentially self-adjointness. However, in many examples the spatial part of the wave operator turns out to be not essentially self-adjoint, but it does satisfy a weaker property that we call here quasi-essentially self-adjointness, which is enough to ensure the desired well-posedness. This is why we also characterize this second property. We state abstract results, then general results for a class of operators encompassing many examples in the literature, and we finish with the explicit analysis of some of them.
Fil: Gamboa Saravi, Ricardo Enrique. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Sanmartino, Marcela. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Tchamitchian, Philippe. Centre National de la Recherche Scientifique; Francia. Aix-Marseille Université; Francia
Materia
Cauchy problem
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/23632
Acceder
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spelling On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimesGamboa Saravi, Ricardo EnriqueSanmartino, MarcelaTchamitchian, PhilippeCauchy problemhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We give simple conditions implying the well-posedness of the Cauchy problem for the propagation of classical scalar fields in general (n + 2)-dimensional static and spherically symmetric spacetimes. They are related to the properties of the underlying spatial part of the wave operator, one of which being the standard essentially self-adjointness. However, in many examples the spatial part of the wave operator turns out to be not essentially self-adjoint, but it does satisfy a weaker property that we call here quasi-essentially self-adjointness, which is enough to ensure the desired well-posedness. This is why we also characterize this second property. We state abstract results, then general results for a class of operators encompassing many examples in the literature, and we finish with the explicit analysis of some of them.Fil: Gamboa Saravi, Ricardo Enrique. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Sanmartino, Marcela. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaFil: Tchamitchian, Philippe. Centre National de la Recherche Scientifique; Francia. Aix-Marseille Université; FranciaIOP Publishing2013-10info: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/11336/23632Gamboa Saravi, Ricardo Enrique; Sanmartino, Marcela; Tchamitchian, Philippe ; On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes; IOP Publishing; Classical and Quantum Gravity; 30; 23; 10-2013; 235014-2350440264-9381CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/0264-9381/30/23/235014info:eu-repo/semantics/altIdentifier/doi/10.1088/0264-9381/30/23/235014info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:12:16Zoai:ri.conicet.gov.ar:11336/23632instacron: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:34982025-10-22 11:12:17.012CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes
title On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes
spellingShingle On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes
Gamboa Saravi, Ricardo Enrique
Cauchy problem
title_short On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes
title_full On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes
title_fullStr On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes
title_full_unstemmed On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes
title_sort On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes
dc.creator.none.fl_str_mv Gamboa Saravi, Ricardo Enrique
Sanmartino, Marcela
Tchamitchian, Philippe
author Gamboa Saravi, Ricardo Enrique
author_facet Gamboa Saravi, Ricardo Enrique
Sanmartino, Marcela
Tchamitchian, Philippe
author_role author
author2 Sanmartino, Marcela
Tchamitchian, Philippe
author2_role author
author
dc.subject.none.fl_str_mv Cauchy problem
topic Cauchy problem
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We give simple conditions implying the well-posedness of the Cauchy problem for the propagation of classical scalar fields in general (n + 2)-dimensional static and spherically symmetric spacetimes. They are related to the properties of the underlying spatial part of the wave operator, one of which being the standard essentially self-adjointness. However, in many examples the spatial part of the wave operator turns out to be not essentially self-adjoint, but it does satisfy a weaker property that we call here quasi-essentially self-adjointness, which is enough to ensure the desired well-posedness. This is why we also characterize this second property. We state abstract results, then general results for a class of operators encompassing many examples in the literature, and we finish with the explicit analysis of some of them.
Fil: Gamboa Saravi, Ricardo Enrique. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Sanmartino, Marcela. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Tchamitchian, Philippe. Centre National de la Recherche Scientifique; Francia. Aix-Marseille Université; Francia
description We give simple conditions implying the well-posedness of the Cauchy problem for the propagation of classical scalar fields in general (n + 2)-dimensional static and spherically symmetric spacetimes. They are related to the properties of the underlying spatial part of the wave operator, one of which being the standard essentially self-adjointness. However, in many examples the spatial part of the wave operator turns out to be not essentially self-adjoint, but it does satisfy a weaker property that we call here quasi-essentially self-adjointness, which is enough to ensure the desired well-posedness. This is why we also characterize this second property. We state abstract results, then general results for a class of operators encompassing many examples in the literature, and we finish with the explicit analysis of some of them.
publishDate 2013
dc.date.none.fl_str_mv 2013-10
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/11336/23632
Gamboa Saravi, Ricardo Enrique; Sanmartino, Marcela; Tchamitchian, Philippe ; On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes; IOP Publishing; Classical and Quantum Gravity; 30; 23; 10-2013; 235014-235044
0264-9381
CONICET Digital
CONICET
url http://hdl.handle.net/11336/23632
identifier_str_mv Gamboa Saravi, Ricardo Enrique; Sanmartino, Marcela; Tchamitchian, Philippe ; On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes; IOP Publishing; Classical and Quantum Gravity; 30; 23; 10-2013; 235014-235044
0264-9381
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://iopscience.iop.org/article/10.1088/0264-9381/30/23/235014
info:eu-repo/semantics/altIdentifier/doi/10.1088/0264-9381/30/23/235014
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv IOP Publishing
publisher.none.fl_str_mv IOP Publishing
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 12.982451

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