The SZ effect from cluster cavities
  In this Letter we derive the SZ effect (SZE) observable in the direction of the giant X-ray cavities found in the atmospheres of galaxy clusters. We explore specifically the case of the cluster MS0735.6+7421. The SZE produced in the cavities embedded in the cluster thermal atmosphere is of non-thermal nature: it dominates the overall cluster SZE at the frequency x_{0,th} - at which the thermal SZE from the cluster vanishes - and appears, at mm and sub-mm frequencies, as a negative SZE located only in the regions of the intracluster space occupied by the cavities. We show that SZ observations, combined with X-ray and radio data, are able to shed light on the morphology, on the physical structure, on the dynamics and the origin of these recently discovered non-thermal features of galaxy clusters. These studies will be also relevant to determine the impact of specific events of the nature of cavities on the use of SZ and X-ray clusters as probes for cosmology and for the large scale structure of the universe. 
S. Colafrancesco