The Dynamics of a Viscous Gas Ring around a Kerr Black Hole

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Abstract
The dynamics of a rotationally symmetric viscous gas ring around a Kerr black hole is calculated in the thin-disk approximation. An evolution equation for the surface density &(t, r) is derived, which is the relativistic extension of a classical equation obtained by R. A singular point appears at the radius Lué st. of the last stable circular orbit The nature of this point is investigated, and it turns out that the r r c . solution is always bounded at and no boundary condition can be obtained at this radius. A unique r c , solution of an initial value problem requires a matching condition at which follows from the —ow r c structure between and the horizon. In the model presented here, the density in this domain is zero, rc and the resulting boundary condition leads to a vanishing shear stress at which is the condition r rc, used in the standard stationary thin-disk model of Novikov & Thorne. Numerical solutions of the evolu- tion equation are presented for two diÜerent angular momenta of the black hole. The time evolution of the resulting accretion rate depends strongly on this angular momentum. Subject headings: accretion, accretion disksblack hole physicshydrodynamicsrelativity

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