  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.
