Alejandro Bellati: Asymptotic stability of the double-cusp spacetime

The long time asymptotic of the cosmological solutions of the Einstein equations has been the subject of intense research since the early years of Einstein's theory. Solutions with global symmetries have been extensively studied and are reasonably understood but outside that realm the understanding is scarce. In this talk I will first introduce the S1xS1-symmetric "double-cusp" vacuum solution, observe its asymptotic behavior, and discuss its stability under perturbations preserving the symmetry. I will then explain how this special solution could be used to construct cosmological solutions where, as time increases, two hyperbolic 3-manifolds separate from each other along a neck. These new solutions would not have neither symmetries nor asymptotic symmetries, and thus would exhibit a radically new type of behavior.