Stable ultracompact objects

Ultra-Compact Objects (UCOS) have been found to be interesting astrophysical entities. The existence of such a possible stable object has been discussed by considering the stability of Tolman's type VII solution which is one of the few physically relevant exact solutions of Einstein's field equations for a static and spherically symmetric mass distribution. A distinctive feature of this solution among the others is that the surface density also drops to zero (i.e., the continuity of density, and the respective derivative of the metric parameter (lambda') is also assured at the surface of the configuration). The stability analysis of this solution, according to the variational method [20], as well as the binding-energy criteria of fluid spheres shows that the configuration remains stable at least up to a central redshift, z(o) less than or equal to 5.09, and surface redshift, z(a) less than or equal to 0.78 (i.e, up to a u (equivalent to mass/size) value less than or equal to 0.3428), thereby confirming the existence of an ultracompact object (UCO) that corresponds to a mass to size ratio (u equivalent to M/a) greater than or equal to 1/3.