Thin disc around a rotating black hole, but with support in-between

Abstract

In the previous paper, we presented the metric obtained from a general Weyl seed using the Belinskii–Zakharov inverse-scattering technique with two real solitons. It describes the field of a stationary black hole surrounded by a source inherited from the seed. In the present paper, we study the solution in further detail with the inverted first Morgan–Morgan counter-rotating disc employed as a seed. In particular, the properties of the horizon, the static limit, the equatorial plane, the extreme limit of the solution and the resulting external disc are analysed and illustrated. It turns out that there is a jump in derivatives of the metric in the equatorial plane even below the seed disc, indicating the presence of a ‘suspension layer’ that confines the system against gravitational collapse or decay. Hence, the solution cannot represent a realistic axisymmetric accretion disc around a rotating black hole.