@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",
targetfile = "araujo_master.pdf",
urlaccessdate = "27 abr. 2024"
}