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@InProceedings{Araújo:2016:MaEqSo,
               author = "Ara{\'u}jo, Jos{\'e} Carlos Neves de",
          affiliation = "{Instituto Nacional de Pesquisas Espaciais (INPE)}",
                title = "Master equation solutions in the linear regime of characteristic 
                         formulation of general relativity",
                 year = "2016",
         organization = "International Conference on General Relativity and Gravitation, 
                         21.",
             abstract = "From the field equations in the linear regime of the 
                         characteristic formulation of general relativity, Bishop, for a 
                         Schwarzschild´s background, and Madler, for a Minkowski´s 
                         background, were able to show that it is possible to derive a 
                         fourth order ordinary differential equation, called master 
                         equation, for the J metric variable of the BondiSachs metric. Once 
                         beta, another Bondi-Sachs potential, is obtained from the field 
                         equations, and J is obtained from the master equation, the other 
                         metric variables are solved integrating directly the rest of the 
                         field equations. In the past, the master equation was solved for 
                         the first multipolar terms, for both the Minkowski´s and 
                         Schwarzschild´s backgrounds. Also, Madler recently reported a 
                         generalization of the exact solutions to the linearised field 
                         equations when a Minkowski´s background is considered, expressing 
                         the master equation family of solutions for the vacuum in terms of 
                         Bessel´s functions of the first and the second kind. Here, we 
                         report new solutions to the master equation for any multipolar 
                         moment l, with and without matter sources in terms only of the 
                         first kind Bessel´s functions for the Minkowski, and in terms of 
                         the Confluent Heun´s functions (Generalised Hypergeometric) for 
                         radiative (nonradiative) case in the Schwarzschild´s background. 
                         We particularize our families of solutions for the known cases for 
                         l =2 reported previously in the literature and find complete 
                         agreement, showing the robustness of our results.",
  conference-location = "New York",
      conference-year = "10-15 July",
             language = "en",
        urlaccessdate = "25 nov. 2020"
}


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