On the runaway instability of relativistic tori⋆

We further investigate the runaway instability of relativistic tori around black holes assuming a power law distribution of the specific angular momentum. We neglect the self-gravity of the torus; thus the gravitational field of the system is determined by the central rotating black hole alone (the Kerr geometry). We find that for any positive (i.e. consistent with the local Rayleigh stability condition) power law index of the angular momentum distribution, the tori are always runaway stable for a sufficiently large spin of the black hole. However, before concluding that some (astrophysically realistic) tori could indeed be runaway stable, one should include, in full general relativity, the destabilizing effect of self-gravity.