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We study the stability of general relativistic static thick disks, as anapplication we consider the thick disk generated by applying the ``displace,cut, fill and reflect" method, usually known as the image method, to theSchwarzschild metric in isotropic coordinates. The isotropic Schwarzschildthick disk obtained from this method is the simplest model to describe, in thecontext of General Relativity, real thick galaxies. The stability under ageneral first order perturbation of the disk is investigated. The first orderperturbation, when applying to the conservation equations, leads to a set ofdifferential equations that are, in general, not self-consistent. This opensthe possibility of performing various kinds of perturbations to transform theresulting system of equations into a self-consistent system. We perform acomplete classification of the perturbations as well as the stability analysisfor all the relevant physical perturbations. We found that, in general, theisotropic Schwarzschild thick disk is stable under these kinds ofperturbations.Comment: 17 page

Stability of general relativistic static thick disks: the isotropic Schwarzschild thick disk