Stability of general relativistic static thick disks: the isotropic Schwarzschild thick disk |
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Authors: | Maximiliano Ujevic Patricio S Letelier |
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Institution: | 1. Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, 09210-170, Santo André, S?o Paulo, Brasil 2. Departamento de Matemática Aplicada, Instituto de Matemática, Estatística e Computa??o Científica, Universidade Estadual de Campinas, 13081-970, Campinas, S?o Paulo, Brasil
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Abstract: | We study the stability of general relativistic static thick disks. As an application we consider the thick disk generated
by applying the “displace, cut, fill and reflect” method, usually known as the image method, to the Schwarzschild metric in
isotropic coordinates. The isotropic Schwarzschild thick disk obtained from this method is the simplest model to describe,
in the context of General Relativity, real thick galaxies. Stability under a general first order perturbation of the disk
energy momentum tensor is investigated. The first order perturbation, when applied to the conservation equations, leads to
a set of differential equations that have fewer equations than unknowns. In this article we search for perturbations in which
the perturbation of the four velocity in a certain direction leads to a pressure perturbation in the same direction. We found
that, in general, the isotropic Schwarzschild thick disk is stable under these kinds of perturbations. |
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