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@PhDThesis{CedeņoMontaņa:2016:LiReCh,
               author = "Cedeņo Montaņa, Carlos Eduardo",
                title = "On the linear regime of the characteristic formulation of general 
                         relativity in the Minkowski and Schwarzschild's backgrounds",
               school = "Instituto Nacional de Pesquisas Espaciais (INPE)",
                 year = "2016",
              address = "S{\~a}o Jos{\'e} dos Campos",
                month = "2016-02-17",
             keywords = "general relativity, characteristic formalism, gravitational waves, 
                         linear regime, relatividade geral, formalismo 
                         caracter{\'{\i}}stico, ondas gravitationais, regime linear.",
             abstract = "We present here the linear regime of the Einstein\${'}\$s field 
                         equations in the characteristic formulation. Through a simple 
                         decomposition of the metric variables in spin-weighted spherical 
                         harmonics, the field equations are expressed as a system of 
                         coupled ordinary differential equations. The process for 
                         decoupling them leads to a simple equation for J - one of the 
                         Bondi-Sachs metric variables - known in the literature as the 
                         master equation. Then, this last equation is solved in terms of 
                         Bessel\${'}\$s functions of the first kind for the Minkowskis 
                         background, and in terms of the Heuns function in the 
                         Schwarzschilds case. In addition, when a matter source is 
                         considered, the boundary conditions across the time-like world 
                         tubes bounding the source are taken into account. These boundary 
                         conditions are computed for all multipole modes. Some examples as 
                         the point particle binaries in circular and eccentric orbits, in 
                         the Minkowskis background are shown as particular cases of this 
                         formalism. RESUMO: N{\'o}s apresentamos aqui o regime linear das 
                         equa{\c{c}}{\~o}es de campo de Einstein na 
                         formula{\c{c}}{\~a}o caracter{\'{\i}}stica. Atrav{\'e}s de 
                         uma decomposi{\c{c}}{\~a}o simples das vari{\'a}veis 
                         m{\'e}tricas em harm{\^o}nicos esf{\'e}ricos com peso de spin, 
                         as equa{\c{c}}{\~o}es de campo s{\~a}o expressas como um 
                         sistema de equa{\c{c}}{\~o}es diferenciais ordin{\'a}rias 
                         acopladas. O processo de desacopl{\'a}-las leva a uma 
                         equa{\c{c}}{\~a}o para J - uma das vari{\'a}veis da 
                         m{\'e}trica de Bondi-Sachs - conhecida na literatura como 
                         equa{\c{c}}{\~a}o mestre. Ent{\~a}o, esta {\'u}ltima 
                         equa{\c{c}}{\~a}o {\'e} resolvida em termos de 
                         fun{\c{c}}{\~o}es de Bessel do primeiro tipo para o fundo de 
                         Minkowski e em termos de fun{\c{c}}{\~o}es de Heun no caso de 
                         Schwarzschild. Al{\'e}m disso, quando uma fonte {\'e} 
                         considerada, as condi{\c{c}}{\~o}es de contorno atrav{\'e}s do 
                         tubo de mundo limitando a fonte {\'e} levada em conta. Essas 
                         condi{\c{c}}{\~o}es de contorno s{\~a}o calculadas para todos 
                         os modos multipolares. Alguns exemplos como bin{\'a}rias em 
                         {\'o}rbita circular e exc{\^e}ntrica no fundo de Minkowski 
                         s{\~a}o mostrados como casos particulares deste formalismo.",
            committee = "Aguiar, Odylio Denys de (presidente) and Ara{\'u}jo, Jos{\'e} 
                         Carlos Neves de (orientador) and Chirenti, Cec{\'{\i}}lia 
                         Bertoni Martha Hadler and Marinho Junior, Rubens de Melo and 
                         Oliveira, Henrique Pereira de and Lima, Jos{\'e} Ademir Sales 
                         de",
           copyholder = "SID/SCD",
         englishtitle = "No regime linear da formula{\c{c}}{\~a}o caracter{\'{\i}}stica 
                         da relatividade geral nos fundos de Minkowski e de Schwarzschild",
             language = "en",
                pages = "181",
                  ibi = "8JMKD3MGP3W34P/3KLMGUB",
                  url = "http://urlib.net/rep/8JMKD3MGP3W34P/3KLMGUB",
           targetfile = "publicacao.pdf",
        urlaccessdate = "27 nov. 2020"
}


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