On the Influence of the Mass Definition in the Stability of Axisymmetric Relativistic Thin Disks

The study on the stability of relativistic disks is one of the most important criteria for the characterization of astrophysically relevant galactic or accretion disks models. In this paper, we perform an analysis of the stability of static axisymmetric relativistic thin disks, by introducing a first-order perturbation into the energy-momentum tensor of the fluid. The formalism is applied to three particular models built with the aid of the displace-cut-reflect (DCR) method, and previously considered in literature (Ujevic and Letelier, 2004), but modifying the mass criteria, i.e., using the Komar mass instead of the total surface mass. Under this conditions, it is found that the total mass values are independent of the parameters of the DCR-method, which let us choose the boundary condition for the cutoff radius, such that it takes the maximum value that allows an appreciable and well-behaved perturbation on the disk. As a general result, we found that the Komar mass is more appropriate to define the cutoff radius.