Nested solutions of gravitational condensate stars

Black holes are normally and naturally associated to the end-point of gravitational collapse. Yet, alternatives have been proposed and a particularly interesting one is that of gravitational condensate stars, or gravastars. We here revisit the gravastar model and increase the degree of speculation by considering new solutions that are inspired by the original model of gravastars with anisotropic pressure, but also offer surprising new features. In particular, we show that it is possible to nest two gravastars into each other and obtain a new solution of the Einstein equations. Since each gravastar essentially behaves as a distinct self-gravitating equilibrium, a large and rich space of parameters exists for the construction of nested gravastars. In addition, we show that these nested-gravastar solutions can be extended to an arbitrarily large number of shells, with a prescription specified in terms of simple recursive relations. Although these ultra-compact objects are admittedly very exotic, some of the solutions found, provide an interesting alternative to a black hole by having a singularity-free origin, a full matter interior, a time-like matter surface, and a compactness $\mathcal{C}\to (1/2)^{-}$.