Relativistic fluid disks in orbit around Kerr black holes

Abstract

The general solution of the relativistic Euler equations for an ideal fluid is presented for the special case of the stationary, axisymmetric, purely azimuthal flow of isentropic fluid in an arbitrary stationary, axisymmetric gravitational field. In leaving the spacetime metric unspecified, the option of imposing Einstein's equations, and thus of taking the effects of self-gravitation into account is retained. As a particular example in which self-gravitation is ignored, the structure of those fluid disks around Kerr black holes which are characterized by constant angular momentum per unit inertial mass is studied. For each allowable equation of state, these solutions describe a two-parameter family of disks which can orbit a given Kerr black hole. Special attention is given to the influence of the black hole's angular momentum upon the structure of the given family of disks. One notable feature these disks exhibit is their pronounced thickness in the direction perpendicular to the equatorial plane of the Kerr field.