A two-mass expanding exact space-time solution
  In order to understand how locally static configurations around
gravitationally bound bodies can be embedded in an expanding universe, we
investigate the solutions of general relativity describing a space-time whose
spatial sections have the topology of a 3-sphere with two identical masses at
the poles. We show that Israel junction conditions imply that two spherically
symmetric static regions around the masses cannot be glued together. If one is
interested in an exterior solution, this prevents the geometry around the
masses to be of the Schwarzschild type and leads to the introduction of a
cosmological constant. The study of the extension of the Kottler space-time
shows that there exists a non-static solution consisting of two static regions
surrounding the masses that match a Kantowski-Sachs expanding region on the
cosmological horizon. The comparison with a Swiss-Cheese construction is also
discussed.
