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*Astron. Astrophys. 331, 1143-1146 (1998)*
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*Research Note*
## On the runaway instability of relativistic tori
^{*}
**
Marek A. Abramowicz **^{ 1, 3, 4},
Vladimír Karas ^{ 2} and
Antonio Lanza ^{ 3}
^{1} Department of Astronomy and Astrophysics, Göteborg
University and Chalmers University of Technology,
S-412 96 Göteborg, Sweden (marek@tfa.fy.chalmers.se)
^{2} Astronomical Institute, Charles University, Faculty of
Mathematics and Physics,
V Holeovikách 2,
CZ-180 00 Praha, Czech Republic (karas@mbox.cesnet.cz)
^{3} Scuola Internazionale Superiore di Studi Avanzati, Via
Beirut 2-4, I-34 014 Trieste, Italy (lanza@sissa.it)
^{4} International Centre for Theoretical Physics, Strada
Costiera 11, I-34 014 Trieste, Italy
*Received 15 September 1997 / Accepted 30 October 1997*
**Abstract**
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.
**Key words:** accretion:
accretion-discs
black hole
physics
instabilities
* Work prepared during The Annual Nordic-Trieste Astrophysics Workshop (ICTP, Trieste 1997)
*Send offprint requests to:* V. Karas
### Contents
© European Southern Observatory (ESO) 1998
Online publication: March 3, 1998
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