ON THE PULSATIONS OF RELATIVISTIC ACCRETION DISKS AND ROTATING STARS - THE COWLING APPROXIMATION

This paper shows that the hydrodynamic degrees of freedom of the adiabatic pulsations of relativistic fluids (e.g., accretion disks or rotating stars) can be described by a single scalar potential. When the gravitational perturbations are neglected-the Cowling approximation-this potential is determined by a second-order (typically elliptic) partial differential equation. A variational principle is developed from which the pulsation frequencies may be evaluated in this approximation. For objects like accretion disks in which self-gravitational effects are negligible, this approximation becomes an exact description of the pulsations.