Gravothermal Catastrophe with a Cosmological Constant

We investigate the effect of a cosmological constant on the gravothermal catastrophe in the Newtonian limit. A negative cosmological constant acts as a thermodynamic destabilizer'. The Antonov radius gets smaller and the instability occurs, not only for negative but also for positive energy values. A positive cosmological constant acts as a stabilizer’ of the system, which, in this case, exhibits a novel reentrant behaviour'. In addition to the Antonov radius we find a second critical radius, where an inverse Antonov transition’ occurs; a series of local entropy maxima is restored.