Isomonodromy method and black holes quasinormal modes : numerical results and extremal limit analysis
Autor(a) principal: | |
---|---|
Data de Publicação: | 2023 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFPE |
Texto Completo: | https://repositorio.ufpe.br/handle/123456789/52269 |
Resumo: | In this thesis, we present and apply the isomonodromy method (or isomon- odromic method) to the study of quasinormal modes, more precisely, we consider the analysis of modes that are associated with linear perturbations in two distinct four- dimensional black holes one with angular momentum (Kerr) and one with charge (Reissner-Nordström). We show, using the method, that the QN frequencies for both black holes can be analyzed with high numerical accuracy and for certain regimes even analytically. We also explore, by means of the equations involved, the regime in which both black holes become extremal. We reveal for this case that through the isomon- odromic method, we can calculate with good accuracy the values for the quasinormal frequencies associated with gravitational, scalar, and electromagnetic perturbations in the black hole with angular momentum, as well as spinorial and scalar perturbations in the charged black hole. Extending thus the analysis of QN frequencies in the regime in which the methods used in the literature have generally convergence problems. Through the separation of variables, we show that the equations describing linear perturbations on both black holes can be rewritten in terms of second-order ordinary differential equations (ODEs), where for the cases in which both black holes are non- extremal and extremal, we have that such ODEs are the confluent and double-confluent Heun equations, respectively. In turn, we consider the matrix representation of the so- lutions of such ODEs and use the method of isomonodromic deformations, which is based on the existence of families of linear matrix systems with the same monodromy parameters that can be deformed isomonodromically. From the method, we derive con- ditions for the isomonodromic functions τV and τIII, which are strictly connected with isomonodromic deformations in the confluent and double-confluent Heun equations, respectively. By means of these conditions, we are able to perform the numerical analy- sis of the QN frequencies for both black holes, in the extremal or non-extremal regime. Subsequently, we show that it can be possible to reformulate, through the isomon- odromic method, the eigenvalue problem of the confluent and double-confluent Heun equations into an initial value problem for both τ-functions. Finally, for the case of the charged Reissner-Nordström black hole, following the same procedure applied to the Kerr black hole, we analyze the values of the QN frequencies for the extremal and non-extremal Reissner-Nordström black hole. For both cases, we present the results for the quasinormal frequencies associated with linear perturbations of charged scalar and spinorial fields. |
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CAVALCANTE, João Paulohttp://lattes.cnpq.br/5000533010369737http://lattes.cnpq.br/8859998369703134CUNHA, Bruno Geraldo Carneiro da2023-09-15T13:10:10Z2023-09-15T13:10:10Z2023-06-30CAVALCANTE, João Paulo. Isomonodromy method and black holes quasinormal modes: numerical results and extremal limit analysis. 2023. Tese (Doutorado em Física) – Universidade Federal de Pernambuco, Recife, 2023.https://repositorio.ufpe.br/handle/123456789/52269In this thesis, we present and apply the isomonodromy method (or isomon- odromic method) to the study of quasinormal modes, more precisely, we consider the analysis of modes that are associated with linear perturbations in two distinct four- dimensional black holes one with angular momentum (Kerr) and one with charge (Reissner-Nordström). We show, using the method, that the QN frequencies for both black holes can be analyzed with high numerical accuracy and for certain regimes even analytically. We also explore, by means of the equations involved, the regime in which both black holes become extremal. We reveal for this case that through the isomon- odromic method, we can calculate with good accuracy the values for the quasinormal frequencies associated with gravitational, scalar, and electromagnetic perturbations in the black hole with angular momentum, as well as spinorial and scalar perturbations in the charged black hole. Extending thus the analysis of QN frequencies in the regime in which the methods used in the literature have generally convergence problems. Through the separation of variables, we show that the equations describing linear perturbations on both black holes can be rewritten in terms of second-order ordinary differential equations (ODEs), where for the cases in which both black holes are non- extremal and extremal, we have that such ODEs are the confluent and double-confluent Heun equations, respectively. In turn, we consider the matrix representation of the so- lutions of such ODEs and use the method of isomonodromic deformations, which is based on the existence of families of linear matrix systems with the same monodromy parameters that can be deformed isomonodromically. From the method, we derive con- ditions for the isomonodromic functions τV and τIII, which are strictly connected with isomonodromic deformations in the confluent and double-confluent Heun equations, respectively. By means of these conditions, we are able to perform the numerical analy- sis of the QN frequencies for both black holes, in the extremal or non-extremal regime. Subsequently, we show that it can be possible to reformulate, through the isomon- odromic method, the eigenvalue problem of the confluent and double-confluent Heun equations into an initial value problem for both τ-functions. Finally, for the case of the charged Reissner-Nordström black hole, following the same procedure applied to the Kerr black hole, we analyze the values of the QN frequencies for the extremal and non-extremal Reissner-Nordström black hole. For both cases, we present the results for the quasinormal frequencies associated with linear perturbations of charged scalar and spinorial fields.CNPqNesta tese, nós apresentamos e aplicamos o método de isomonodrômia (ou método isomonodrômico) no estudo dos modos quase-normais, mais precisamente consideramos a análise dos modos que estão associados com perturbações lineares em dois buracos negros quadridimensionais distintos um com momento angular (Kerr) e outro com carga (Reissner-Nordström). Mostramos, por meio do método, que as frequências QN para ambos os buracos negros podem ser analisadas com alta pre- cisão numérica e para certos regimes até mesmo de maneira analítica. Exploramos também, por meio das equações envolvidas o regime no qual ambos os buracos negros tornam-se extremais. Revelamos para esse caso que através do método isomonodrômico conseguimos calcular com boa precisão os valores para as frequências quase-normais associadas com perturbações gravitacionais, escalares e eletromagnéticas no buraco ne- gro com momento angular, bem como perturbações espinoriais e escalares no buraco negro com carga. Estendendo assim a análise das frequências QN no regime no qual os métodos utilizados na literatura apresentam geralmente problemas de convergência. Mostramos, através de separação de variáveis, que as equações que descrevem per- turbações lineares em ambos os buracos negros podem ser reescritas em termos de equações diferenciais ordinárias (EDOs) de segunda ordem, onde, para os casos em que ambos os buracos negros são não extremais e extremais, temos que tais EDOs são as equações de Heun confluente e biconfluente, respectivamente. Por sua vez, consid- eramos a representação matricial das soluções de tais EDOs e utilizamos o método das deformações isomonodrômicas, que fundamenta-se na existência de famílias de sistemas matriciais lineares com os mesmos parâmetros de monodromia e que podem ser deformados isomonodromicamente. A partir do método, derivamos condições para as funções isomonodrômicas τV e τIII, que estão estritamente ligadas com deformações isomonodrômicas nas equações de Heun confluent e biconfluente, respectivamente. Por meio dessas condições conseguimos fazer a análise numérica das frequências QN para ambos os buracos buraco negros, sendo eles extremais ou não. Posteriomente, fazendo uso da representação das duas funções τV e τIII em termos do determinante de Fredholm, mostramos que podemos reformular, através do método isomonodrômico, o problema de autovalores das equacões de Heun confluente e biconfluente em um problema de valor inicial para ambas as funções τ. Finalmente, para o caso do buraco negro carregado de Reissner-Nordström, seguindo o mesmo procedimento aplicado para o buraco negro de Kerr, analisamos os valores das frequências QN para os casos de Reissner-Nordström extremal e não-extremal. Apresentamos, para ambos os casos, os resultados para as frequências quase-normais associadas com perturbações lineares de campos escalares e espinorias carregados.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em FisicaUFPEBrasilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessFísica teórica e computacionalPerturbações linearesModos quase-normaisDeformações isomonodrômicasIsomonodromy method and black holes quasinormal modes : numerical results and extremal limit analysisinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisdoutoradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPEORIGINALTESE João Paulo Cavalcante.pdfTESE João Paulo Cavalcante.pdfapplication/pdf2888996https://repositorio.ufpe.br/bitstream/123456789/52269/1/TESE%20Jo%c3%a3o%20Paulo%20Cavalcante.pdf70e8155f260368a5702848d01bb18c7bMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufpe.br/bitstream/123456789/52269/2/license_rdfe39d27027a6cc9cb039ad269a5db8e34MD52LICENSElicense.txtlicense.txttext/plain; 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dc.title.pt_BR.fl_str_mv |
Isomonodromy method and black holes quasinormal modes : numerical results and extremal limit analysis |
title |
Isomonodromy method and black holes quasinormal modes : numerical results and extremal limit analysis |
spellingShingle |
Isomonodromy method and black holes quasinormal modes : numerical results and extremal limit analysis CAVALCANTE, João Paulo Física teórica e computacional Perturbações lineares Modos quase-normais Deformações isomonodrômicas |
title_short |
Isomonodromy method and black holes quasinormal modes : numerical results and extremal limit analysis |
title_full |
Isomonodromy method and black holes quasinormal modes : numerical results and extremal limit analysis |
title_fullStr |
Isomonodromy method and black holes quasinormal modes : numerical results and extremal limit analysis |
title_full_unstemmed |
Isomonodromy method and black holes quasinormal modes : numerical results and extremal limit analysis |
title_sort |
Isomonodromy method and black holes quasinormal modes : numerical results and extremal limit analysis |
author |
CAVALCANTE, João Paulo |
author_facet |
CAVALCANTE, João Paulo |
author_role |
author |
dc.contributor.authorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/5000533010369737 |
dc.contributor.advisorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/8859998369703134 |
dc.contributor.author.fl_str_mv |
CAVALCANTE, João Paulo |
dc.contributor.advisor1.fl_str_mv |
CUNHA, Bruno Geraldo Carneiro da |
contributor_str_mv |
CUNHA, Bruno Geraldo Carneiro da |
dc.subject.por.fl_str_mv |
Física teórica e computacional Perturbações lineares Modos quase-normais Deformações isomonodrômicas |
topic |
Física teórica e computacional Perturbações lineares Modos quase-normais Deformações isomonodrômicas |
description |
In this thesis, we present and apply the isomonodromy method (or isomon- odromic method) to the study of quasinormal modes, more precisely, we consider the analysis of modes that are associated with linear perturbations in two distinct four- dimensional black holes one with angular momentum (Kerr) and one with charge (Reissner-Nordström). We show, using the method, that the QN frequencies for both black holes can be analyzed with high numerical accuracy and for certain regimes even analytically. We also explore, by means of the equations involved, the regime in which both black holes become extremal. We reveal for this case that through the isomon- odromic method, we can calculate with good accuracy the values for the quasinormal frequencies associated with gravitational, scalar, and electromagnetic perturbations in the black hole with angular momentum, as well as spinorial and scalar perturbations in the charged black hole. Extending thus the analysis of QN frequencies in the regime in which the methods used in the literature have generally convergence problems. Through the separation of variables, we show that the equations describing linear perturbations on both black holes can be rewritten in terms of second-order ordinary differential equations (ODEs), where for the cases in which both black holes are non- extremal and extremal, we have that such ODEs are the confluent and double-confluent Heun equations, respectively. In turn, we consider the matrix representation of the so- lutions of such ODEs and use the method of isomonodromic deformations, which is based on the existence of families of linear matrix systems with the same monodromy parameters that can be deformed isomonodromically. From the method, we derive con- ditions for the isomonodromic functions τV and τIII, which are strictly connected with isomonodromic deformations in the confluent and double-confluent Heun equations, respectively. By means of these conditions, we are able to perform the numerical analy- sis of the QN frequencies for both black holes, in the extremal or non-extremal regime. Subsequently, we show that it can be possible to reformulate, through the isomon- odromic method, the eigenvalue problem of the confluent and double-confluent Heun equations into an initial value problem for both τ-functions. Finally, for the case of the charged Reissner-Nordström black hole, following the same procedure applied to the Kerr black hole, we analyze the values of the QN frequencies for the extremal and non-extremal Reissner-Nordström black hole. For both cases, we present the results for the quasinormal frequencies associated with linear perturbations of charged scalar and spinorial fields. |
publishDate |
2023 |
dc.date.accessioned.fl_str_mv |
2023-09-15T13:10:10Z |
dc.date.available.fl_str_mv |
2023-09-15T13:10:10Z |
dc.date.issued.fl_str_mv |
2023-06-30 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
CAVALCANTE, João Paulo. Isomonodromy method and black holes quasinormal modes: numerical results and extremal limit analysis. 2023. Tese (Doutorado em Física) – Universidade Federal de Pernambuco, Recife, 2023. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufpe.br/handle/123456789/52269 |
identifier_str_mv |
CAVALCANTE, João Paulo. Isomonodromy method and black holes quasinormal modes: numerical results and extremal limit analysis. 2023. Tese (Doutorado em Física) – Universidade Federal de Pernambuco, Recife, 2023. |
url |
https://repositorio.ufpe.br/handle/123456789/52269 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
dc.publisher.program.fl_str_mv |
Programa de Pos Graduacao em Fisica |
dc.publisher.initials.fl_str_mv |
UFPE |
dc.publisher.country.fl_str_mv |
Brasil |
publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFPE instname:Universidade Federal de Pernambuco (UFPE) instacron:UFPE |
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Universidade Federal de Pernambuco (UFPE) |
instacron_str |
UFPE |
institution |
UFPE |
reponame_str |
Repositório Institucional da UFPE |
collection |
Repositório Institucional da UFPE |
bitstream.url.fl_str_mv |
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