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.
Highlights
Introduction and summaryDescription of false vacuum decay in the presence of a black hole (BH) is a long-standing problem [1,2,3,4]
We provide a method to calculate the rate of false vacuum decay induced by a black hole
In this paper we have developed an approach for the analysis of false vacuum decay in BH background
Summary
Description of false vacuum decay in the presence of a black hole (BH) is a long-standing problem [1,2,3,4]. In the case of a Schwarzschild BH this leads to the theory in the cigar-like geometry with compactified Euclidean time coordinate playing the role of the angular variable and the radial coordinate covering the region outside the horizon [28] This picture corresponds to the partition function in the Hartle-Hawking vacuum, i.e., an equilibrium thermal state. The boundary conditions at t → −∞ for the tunneling solutions describing decay of a false vacuum are dictated by the time-ordered Green’s function in this vacuum We argue that this result is general: it is valid for arbitrary geometry and any state with a Gaussian density matrix in the vicinity of the false vacuum.
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