Advection-Dominated Accretion Flow in the Kerr Metric: Propagation of a Wave Pattern

The time evolution of an advection-dominated accretion flow is explored in terms of relativistic fluid equations. An axially symmetric, vertically averaged mean flow is constructed and perturbed. An axisymmetric pattern is followed as it propagates in the form of a wave towards the horizon of a rotating black hole. Several assumptions are relaxed in comparison with previous works (Manmoto et al. 1996, AAA 65.067.206). The wave reflection and steepening are examined and the influence of black hole angular momentum is discussed.