The oscillatory shape of the stationary twisted disc around a Kerr black hole

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Abstract
We consider the twisted accretion disc around a Kerr black hole and derive the stationary twist equation in the leading order on small parameters of relative thickness δ, viscosity α and relativistic corrections rg/r. We take into account post-Newtonian corrections which determine the shape of the stationary twisted accretion disc in the limit of small viscosity, α < δ4/5. We find the phenomenon of radial oscillations of the disc inclination angle β(r) due to this correction. The period of the oscillations is about Δr ≈ δ−4/5rg and decreases with decreasing distance r. We present a qualitative analysis of the oscillatory behaviour and conclude that the oscillations are likely to destroy a disc of low viscosity at sufficiently small r<rf≈δ−3β(∞ )8/3rg. We suggest that the twisted disc might be in a highly turbulent state with α ≈ 1 at r < rf.

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