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We numerically investigate spherically symmetric collapses in theGross-Pitaevskii equation with attractive nonlinearity in a harmonic potential.Even below threshold for direct collapse, the wave function bounces off fromthe origin and may eventually become singular after a number of oscilla- tionsin the trapping potential. This is reminiscent of the evolution of Einsteingravity sourced by a scalar field in Anti-de Sitter space where collapsecorresponds to black hole formation. We carefully examine the long timeevolution of the wave function for continuous families of initial states inorder to sharpen out this qualitative coincidence which may bring new insightsin both directions. On one hand, we comment on possible implications for theso-called Bosenova collapses in cold atom Bose-Einstein condensates. On theother hand, Gross-Pitaevskii provides a toy model to study the relevance ofeither the resonance conditions or the nonlinearity for the problem of Anti-deSitter instability.

Delayed collapses of BECs in relation to AdS gravity