Four-dimensional Traversable Wormholes and Bouncing Cosmologies in
  Vacuum
  In this letter we point out the existence of solutions to General Relativity
with a negative cosmological constant in four dimensions, which contain
solitons as well as traversable wormholes. The latter connect two
asymptotically locally AdS$_{4}$ spacetimes. At every constant value of the
radial coordinate the spacetime is a spacelike warped AdS$_{3}$. We compute the
dual energy momentum tensor at each boundary showing that it yields different
results. We also show that these vacuum wormholes can have more than one throat
and that they are indeed traversable by computing the time it takes for a light
signal to go from one boundary to the other, as seen by a geodesic observer. We
generalize the wormholes to include rotation and charge. When the cosmological
constant is positive we find a cosmology that is everywhere regular, has either
one or two bounces and that for late and early times matches the
Friedmann-Lema\^{\i}tre-Robertson-Walker metric with spherical topology.
