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.