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For the first time ever, we derive equations governing the time-evolution offully relativistic slim accretion disks in the Kerr metric, and numericallyconstruct their detailed non-stationary models. We discuss applications ofthese general results to a possible limit-cycle behavior of thermally unstabledisks. Our equations and numerical method are applicable in a wide class ofpossible viscosity prescriptions, but in this paper we use a diffusive form ofthe "standard alpha prescription" that assumes the viscous torque isproportional to the total pressure. In this particular case, we find that theparameters which dominate the limit-cycle properties are the mass-supply rateand the value of the alpha-viscosity parameter. Although the duration of thecycle (or the outburst) does not exhibit any clear dependence on the black holespin, the maximal outburst luminosity (in the Eddington units) is positivelycorrelated with the spin value. We suggest a simple method for a rough estimateof the black hole spin based on the maximal luminosity and the ratio ofoutburst to cycle durations. We also discuss a temperature-luminosity relationfor the Kerr black hole accretion discs limit-cycle. Based on these results wediscuss the limit-cycle behavior observed in microquasar GRS 1915+105. We alsoextend this study to several non-standard viscosity prescriptions, including a"delayed heating" prescription recently stimulated by the recent MHDsimulations of accretion disks.

the astrophysical journal. supplement series/astrophysical journal. supplement series

Studies of Thermally Unstable Accretion Disks around Black Holes with  Adaptive Pseudospectral Domain Decomposition Method. II. Limit-Cycle Behavior  in accretion disks around Kerr black holes