Black hole induced false vacuum decay from first principles

Abstract

We provide a method to calculate the rate of false vacuum decay induced by a black hole. The method uses complex tunneling solutions and consistently takes into account the structure of different quantum vacua in the black hole metric via boundary conditions. The latter are connected to the asymptotic behavior of the time-ordered Green’s function in the corresponding vacua. We illustrate the technique on a two-dimensional toy model of a scalar field with inverted Liouville potential in an external background of a dilaton black hole. We analytically derive the exponential suppression of tunneling from the Boulware, Hartle-Hawking and Unruh vacua and show that they are parametrically different. The Unruh vacuum decay rate is exponentially smaller than the decay rate of the Hartle-Hawking state, though both rates become unsuppressed at high enough black hole temperature. We interpret the vanishing suppression of the Unruh vacuum decay at high temperature as an artifact of the two-dimensional model and discuss why this result can be modified in the realistic case of black holes in four dimensions.

Black hole induced false vacuum decay: the role of greybody factors

“…In the model of [41], the exponential suppression of the Unruh vacuum decay rate vanishes at high temperatures. We would like to see if this result holds also in a realistic case like the Schwarzschild BH in four dimensions.…”

“…In ref. [41] we have suggested a method to compute the Unruh vacuum decay rate using complex tunneling solutions [42][43][44][45][46]. 1 The method accounts for the quantum state of the false vacuum and, hence, it allows one to discriminate between the Hartle-Hawking and Unruh vacua.…”

“…For explicit calculations ref. [41] adopted a toy two-dimensional model consisting of a real scalar field in the background of a dilaton BH. 2 Thanks to the choice of the tunneling potential, bounce solutions and associated decay rates were found analytically, both for the Hartle-Hawking and Unruh vacua, and both in the BH vicinity and far from it.…”

“…We would like to see if this result holds also in a realistic case like the Schwarzschild BH in four dimensions. The model of [41] lacks two important features of the realistic setup. First, a field in Schwarzschild background feels a centrifugal barrier whose height is inversely proportional to the square of the BH size and, hence, grows with the BH temperature.…”

The Boring Monopole

“…This idea can be generalised to other topological defects such as global monopoles, strings [19][20][21] and domain walls. The defect need not be topologically stable [22,23] and there exist studies of Q-balls [24][25][26] and black holes as nucleation sites [27][28][29][30][31][32] which can affect the electroweak lifetime [33][34][35][36][37]. The gravitational effect of compact objects was considered in [38] and finite density effects in [39].…”