  The recent developments of microgravity experiments with ultracold atoms have
produced a relevant boost in the study of shell-shaped ellipsoidal
Bose-Einstein condensates. For realistic bubble-trap parameters, here we
calculate the critical temperature of Bose-Einstein condensation, which, if
compared to the one of the bare harmonic trap with the same frequencies, shows
a strong reduction. We simulate the zero-temperature density distribution with
the Gross-Pitaevskii equation, and we study the free expansion of the hollow
condensate. While part of the atoms expands in the outward direction, the
condensate self-interferes inside the bubble trap, filling the hole in
experimentally observable times. For a mesoscopic number of particles in a
strongly interacting regime, for which more refined approaches are needed, we
employ quantum Monte Carlo simulations, proving that the nontrivial topology of
a thin shell allows superfluidity. Our work constitutes a reliable benchmark
for the forthcoming scientific investigations with bubble traps.
