On the equivalence of spacetimes, the Cartan-Karlhede algorithm

Detalhes bibliográficos
Autor(a) principal: Mergulhão,Thiago Muniz
Data de Publicação: 2020
Outros Autores: Batista,Carlos
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Revista Brasileira de Ensino de Física (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172020000100437
Resumo: Abstract It is well known that in general relativity theory two spacetimes whose metrics are related by a coordinate transformation are physically equivalent. However, given two line elements, it is virtually impossible to implement the most general coordinate transformation in order to check the equivalence of the spacetimes. In this paper we present the so-called Cartan-Karlhede algorithm, which provides a finite sequence of steps to decide whether or not two metrics are equivalent. The point of this note is to illustrate the method through several simple examples, so that the reader can learn the fundamentals and details of the algorithm in practice.
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spelling On the equivalence of spacetimes, the Cartan-Karlhede algorithmEquivalence of spacetimesCartan algorithmCoordinate transformationsAbstract It is well known that in general relativity theory two spacetimes whose metrics are related by a coordinate transformation are physically equivalent. However, given two line elements, it is virtually impossible to implement the most general coordinate transformation in order to check the equivalence of the spacetimes. In this paper we present the so-called Cartan-Karlhede algorithm, which provides a finite sequence of steps to decide whether or not two metrics are equivalent. The point of this note is to illustrate the method through several simple examples, so that the reader can learn the fundamentals and details of the algorithm in practice.Sociedade Brasileira de Física2020-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172020000100437Revista Brasileira de Ensino de Física v.42 2020reponame:Revista Brasileira de Ensino de Física (Online)instname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/1806-9126-rbef-2020-0041info:eu-repo/semantics/openAccessMergulhão,Thiago MunizBatista,Carloseng2020-05-27T00:00:00Zoai:scielo:S1806-11172020000100437Revistahttp://www.sbfisica.org.br/rbef/https://old.scielo.br/oai/scielo-oai.php||marcio@sbfisica.org.br1806-91261806-1117opendoar:2020-05-27T00:00Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)false
dc.title.none.fl_str_mv On the equivalence of spacetimes, the Cartan-Karlhede algorithm
title On the equivalence of spacetimes, the Cartan-Karlhede algorithm
spellingShingle On the equivalence of spacetimes, the Cartan-Karlhede algorithm
Mergulhão,Thiago Muniz
Equivalence of spacetimes
Cartan algorithm
Coordinate transformations
title_short On the equivalence of spacetimes, the Cartan-Karlhede algorithm
title_full On the equivalence of spacetimes, the Cartan-Karlhede algorithm
title_fullStr On the equivalence of spacetimes, the Cartan-Karlhede algorithm
title_full_unstemmed On the equivalence of spacetimes, the Cartan-Karlhede algorithm
title_sort On the equivalence of spacetimes, the Cartan-Karlhede algorithm
author Mergulhão,Thiago Muniz
author_facet Mergulhão,Thiago Muniz
Batista,Carlos
author_role author
author2 Batista,Carlos
author2_role author
dc.contributor.author.fl_str_mv Mergulhão,Thiago Muniz
Batista,Carlos
dc.subject.por.fl_str_mv Equivalence of spacetimes
Cartan algorithm
Coordinate transformations
topic Equivalence of spacetimes
Cartan algorithm
Coordinate transformations
description Abstract It is well known that in general relativity theory two spacetimes whose metrics are related by a coordinate transformation are physically equivalent. However, given two line elements, it is virtually impossible to implement the most general coordinate transformation in order to check the equivalence of the spacetimes. In this paper we present the so-called Cartan-Karlhede algorithm, which provides a finite sequence of steps to decide whether or not two metrics are equivalent. The point of this note is to illustrate the method through several simple examples, so that the reader can learn the fundamentals and details of the algorithm in practice.
publishDate 2020
dc.date.none.fl_str_mv 2020-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172020000100437
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172020000100437
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/1806-9126-rbef-2020-0041
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Física
publisher.none.fl_str_mv Sociedade Brasileira de Física
dc.source.none.fl_str_mv Revista Brasileira de Ensino de Física v.42 2020
reponame:Revista Brasileira de Ensino de Física (Online)
instname:Sociedade Brasileira de Física (SBF)
instacron:SBF
instname_str Sociedade Brasileira de Física (SBF)
instacron_str SBF
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reponame_str Revista Brasileira de Ensino de Física (Online)
collection Revista Brasileira de Ensino de Física (Online)
repository.name.fl_str_mv Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)
repository.mail.fl_str_mv ||marcio@sbfisica.org.br
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