Self-gravitating thin discs around rotating black holes

Summary

Abstract. We have constructed sequences of equilibrium numerical models for selfgravitating thin discs around rotating black holes. The multigrid method has been used for solving numerically the stationary and axisymmetric Einstein equations describing the problem.

INTRODUCTION

We solved numerically Einstein's equations for equilibrium configurations made by self–gravitating thin discs around rapidly rotating black holes. These configurations may play an important role in modelling active galactic nuclei (AGN) since the self–gravity may induce the so–called “runaway” instability which may be connected with X–ray variability observed in AGNs (Abramowicz et al., 1980, see however Wilson, 1984). Also, such configurations are seen formed in numerical simulations of general relativistic collapse to a black hole (Nakamura, 1981, Stark and Piran, 1986, Nakamura et al., 1987) for some intial conditions.

We consider here only the case in which the disc is thin; for pressure dominated discs (thick discs) work is in progress (see Nishida, Eriguchi and Lanza, 1992). Self–gravitating discs and rings have been considered in the past by Bardeen and Wagoner (1971) (BW) without central body; Will (1974, 1975) has studied weakly self–gravitating rings around slowly rotating black holes.

In order to solve such a highly non–linear problem we employed the multigrid method (MG) as a strategy to solve the finite difference equations which derive from the discretization of Einstein's equations.