ADVECTION-DOMINATED ACCRETION FLOWS IN THE KERR METRIC - I - BASIC EQUATIONS

We write and solve equations describing steady state, optically thin, advection-dominated accretion onto a Kerr black hole. The mean flow, d escribed by the relativistic fluid equations, is axisymmetric and vert ically averaged. The effect of turbulence in the flow is represented b y a viscous shear stress. Our treatment differs in several important w ays from earlier work: we use a causal prescription for the shear stre ss; we do not assume that the relativistic enthalpy is unity (this is important for rapidly rotating holes); and we use a relativistic equat ion of state. We present several representative solutions and use them to evaluate the importance of relativistic effects, to check our appr oximations, and to evaluate the robustness of the input physics. Detai led properties of the solutions are described in an accompanying paper .