Abstract
We study non-perturbative instabilities of AdS spacetime in General Relativity with a cosmological constant in arbitrary dimensions. In this simple setup we explicitly construct a class of gravitational instantons generalizing Witten’s bubble of nothing. We calculate the corresponding Euclidean action and show that its change is finite. The expansion of these bubbles is described by a lower-dimensional de Sitter geometry within a non- compact foliation of the background spacetime. Moreover we discuss the existence of covariantly constant spinors as a possible topological obstruction for such decays to occur. This mechanism is further connected to the stability of supersymmetric vacua in string theory.
Highlights
JHEP08(2020)040 gravity as the weakest force is investigated
By adopting the approach of the swampland conjectures, the existence of metastable de Sitter vacua within a consistent theory of quantum gravity has been called into question
If these conjectures are correct, they may be reconciled with current observations by realizing dark energy in the form of a quintessence supported by time-dependent scalar fields, or by effectively describing it as a braneworld cosmology which is intrinsically evolving in time
Summary
In lieu of a full dynamical treatment of the possible ground states of a gravitational system of a theory of quantum gravity, we use the semi-classical approximation to assess possible quantum instabilities of the vacuum. Ρ → +∞, we recover the KK vacuum, in the interior, the presence of the Schwarzschild warp factors and the range of ρ ∈ (R, +∞) indicate that the (ρ, τ )-plane parametrizes the exterior region of a hyperbola of radius R This hyperbola is exactly a de Sitter manifold dS3 which describes a bubble expanding under constant proper acceleration. The solution (2.5) constitutes an instanton describing a non-perturbative instability of the KK vacuum which leads to a bubble of nothing expanding on a de Sitter hyperbola and eventually “eating” the entire KK vacuum The fact that this decay will happen with probability equal to one in an infinite volume of space can be seen by computing a finite difference in Euclidean actions πR2 ∆SE = 4 G(N4). Since this analysis has been performed in the semi-classical approximation, we can only trust the interpretation of the decay for values of R that are large with respect to the Planck length, Pl
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