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

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 delta, viscosity alpha and relativistic corrections r(g)/r. We take into account post-Newtonian corrections which determine the shape of the stationary twisted accretion disc in the limit of small viscosity, alpha < delta(4/5). We find the phenomenon of radial oscillations of the disc inclination angle beta(r) due to this correction. The period of the oscillations is about Delta r approximate to delta(-4/5)r(g) 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 < r(f) approximate to delta(-3)beta(infinity)(8/3)r(g). We suggest that the twisted disc might be in a highly turbulent state with alpha approximate to 1 at r < r(f).