  We show that there is a classical metric satisfying the Einstein equations
outside a finite spacetime region where matter collapses into a black hole and
then emerges from a white hole. We compute this metric explicitly. We show how
quantum theory determines the (long) time for the process to happen. A black
hole can thus quantum-tunnel into a white hole. For this to happen, quantum
gravity should affect the metric also in a small region outside the horizon: we
show that contrary to what is commonly assumed, this is not forbidden by
causality or by the semiclassical approximation, because quantum effects can
pile up over a long time. This scenario alters radically the discussion on the
black hole information puzzle.
