Creation of an inflationary universe out of a black hole

We discuss a two-step mechanism to create a new inflationary domain beyond a wormhole throat which is created by a phase transition around an evaporating black hole. The first step is creation of a false vacuum bubble with a thin-wall boundary by the thermal effects of Hawking radiation. Then this wall induces a quantum tunneling to create a wormhole-like configuration. As the space beyond the wormhole throat can expand exponentially, being filled with false vacuum energy, this may be interpreted as creation of another inflationary universe in the final stage of the black hole evaporation.