J. Ehlers et W. Rindler, SUCCESSIVE SCHWARZSCHILD SPHERES AND OTHER RIGIDITY FRONTIERS IN SPHERICALLY SYMMETRICAL DUST-PLUS-VACUUM SPACETIMES, Physics letters. A, 180(3), 1993, pp. 197-202
Just outside a Schwarzschild sphere concentric rigid test matter spher
es can persist while just inside they cannot. We construct spacetimes
containing successive Schwarzschild spheres and show that there exist
similar but moving rigidity frontiers between them. Some of our soluti
ons exemplify inextensible nonempty spacetimes with Kruskal-like topol
ogy having two asymptotically flat ends of possibly different Schwarzs
child (=ADM) mass.