A study of stability of rotating fluid disks using a variational principle

Stability of non-self gravitating, non-accreting fluid disk rotating around a Schwarzschild black hole is studied by using a variational principle. We find a set of solutions which depending on the value of a parameter, either a stable or an unstable specific angular momentum distribution (Rayleigh's criterion). Using these solutions we find that the calculations based on the variational principle yield results which agree with the Rayleigh criteria when a suitable choice of the trial function is made.