O(3)-symmetric tunneling at false vacuum decay in general relativity

The O(3)-symmetric vacuum decay is investigated in general relativity in thin-wall approximation. The following processes are studied: the spontaneous nucleation of a new phase bubble containing a remnant of an old phase inside; a subbarrier transition of a new phase bubble with the non-vanishing total energy from a subcritical state to the infinite expansion; the vacuum decay in the vicinity of a black hole; the creation from nothing of the Universe containing a bubble. General formulae for bounces for all these processes are derived. (orig.)