Local stability in general relativity

This paper presents a unified treatment of the problem of local adiabatic stability for stationary, axisymmetric, perfect fluid configurations in general relativity. Criteria for both dynamical and secular stability are obtained via energy principles, without reference to the existence of normal modes. In general, the criteria that obtain are straight forward generalizations of Newtonian results. However, one new purely relativistic effect arise rise: if Eulerian variations in pressure cannot be neglected, there exists the possibility of an additional secular instabiilty toward viscosity unless one imposes a ''causality'' assumption, namely that the velocity of sound be less than unity