Abstract
Static oscillating bounces in Schwarzschild de Sitter spacetime are investigated. The oscillating bounce with many oscillations gives a super-thick bubble wall, for which the total vacuum energy increases while the mass of the black hole decreases due to the conservation of Arnowitt-Deser-Misner (ADM) mass. We show that the transition rate of such an “up-tunneling” consuming the seed black hole is higher than that of the Hawking- Moss transition. The correspondence of analyses in the static and global coordinates in the Euclidean de Sitter space is also investigated.
Highlights
Systems, and a modern interpretation of the HM instanton is that it represents a thermal fluctuation within a horizon volume at the temperature of de Sitter space [18]
The oscillating bounce with k-times crossing is allowed for β ≥ βk as is shown in figure 5
We find out that the vacuum decay rate for the oscillating bounce is in good agreement with that of the BHHM bounce, and in the low mass limit (GM+H+ 1) it is consistent with the Boltzmann factor e∆Mbh/Tav
Summary
The O(4) symmetric oscillating bounce solutions were analysed close to the critical limit of (1.1) by Hackworth and Weinberg [19]. With the geometry corrected at order O(δφ2) They analysed this scalar equation in the dS background, discovering that it yielded an eigenvalue equation for β = 3V (φtop)/(8πGVtop), a lower bound on β for the oscillating bounce solutions, where Vtop ≡ V (φtop). This eigenvalue equation represents solutions for δφ that remain fully within the perturbative regime, does not mean there are no solutions for other values of β, only that these will enter the regime in which the nonlinear corrections to V (φ) become important, as described below. The analytic continuation of the global patch as written here (which is for the convenience of the CDL instanton), T → iTE, while sending X0 → XE0 , is a rotation in the X0,2−4 coordinates, whereas the analytic continuation of the static patch, t → iτ , corresponds to a continuation in the {X0, X1} plane
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