Stars on orbits with pericenters sufficiently close to the supermassive black hole at the center of their host galaxy can be ripped apart by tidal stresses. Some of the resulting stellar debris becomes more tightly bound to the hole and can potentially produce an observable flare called a tidaldisruption event (TDE). We provide a self-consistent, unified treatment of TDEs by non-spinning (Schwarzschild) black holes, investigating several effects of general relativity including changes to the boundary in phase space that defines the loss-cone orbits on which stars are tidally disrupted or captured. TDE rates decrease rapidly at large black-hole masses due to direct stellar capture, but this effect is slightly countered by the widening of the loss cone due to the stronger tidal fields in general relativity. We provide a new mapping procedure that translates between Newtonian gravity and general relativity, allowing us to better compare predictions in both gravitational theories. Partial tidal disruptions in relativity will strip more material from the star and produce more tightly bound debris than in Newtonian gravity for a stellar orbit with the same angular momentum. However, for deep encounters leading to full disruption in both theories, the stronger tidal forces in relativity imply that the star is disrupted further from the black hole and that the debris is therefore less tightly bound, leading to a smaller peak fallback accretion rate. We also examine the capture of tidal debris by the horizon and the relativistic pericenter precession of tidal debris, finding that black holes of 10 6 solar masses and above generate tidal debris precessing by 10• or more per orbit.

In this study it is investigated how variable viscosity affects the onset of instability in the Rayleigh-Bénard convection. An asymptotic approach provides results that are independent of specific property laws. They are compared to those of other studies and to direct solutions of the non-expanded stability equations for particular property laws. It is demonstrated that one can also get the asymptotic results from solutions of the non-expanded equations by use of a so-called combined method. The asymptotic results are general in nature and hold for all Newtonian fluids and all (small) heat transfer rates.

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