```@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"
}

```