nucleate, the bubble must overcome an energy barrier of height where is the difference in energy between the true and false vacuums, is the unknown (possibly extremely large) surface tension of the domain wall, and is the radius of the bubble. Rewriting gives the critical radius as A bubble smaller than the critical size can overcome the potential barrier via quantum tunnelling of instantons to lower energy states. For a large potential barrier, the tunneling rate per unit volume of space is given by where is the reduced Planck constant. As soon as a bubble of lower-energy vacuum grows beyond the critical radius defined by , the bubble's wall will begin to accelerate outward. Due to the typically large difference in energy between the false and true vacuums, the speed of the wall approaches the speed of light extremely quickly. The bubble does not produce any gravitational effects because the negative energy density of the bubble interior is cancelled out by the positive kinetic energy of the wall. Small bubbles of true vacuum can be inflated to critical size by providing energy, although required energy densities are several orders of magnitude larger than what is attained in any natural or artificial process. It is also thought that certain environments can catalyze bubble formation by lowering the potential barrier. Bubble wall has a finite thickness, depending on ratio between energy barrier and energy gain obtained by creating true vacuum. In the case when potential barrier height between true and false vacua is much smaller than energy difference between vacua, shell thickness become comparable with critical radius. Nucleation seeds In general, gravity is believed to stabilize a false vacuum state, at least for transition from (de Sitter space) to (Anti-de Sitter space), while topological defects including cosmic strings and magnetic monopoles may enhance decay probability. Black holes as nucleation seeds In a study in 2015, it was pointed out that the vacuum decay rate could be vastly increased in the vicinity of black holes, which would serve as a nucleation seed. According to this study, a potentially catastrophic vacuum decay could be triggered at any time by primordial black holes, should they exist. The authors note however that if primordial black holes cause a false vacuum collapse then it should have happened long before humans evolved on Earth. A subsequent study in 2017 indicated that the bubble would collapse into a primordial