Abstract
We present a covariant euclidean wormhole solution to Einstein Yang-Mills system and study scalar perturbations analytically. The fluctuation operator has a positive definite spectrum. We compute the Euclidean Green's function, which displays maximal antipodal correlation on the smallest three sphere. Upon analytic continuation, it corresponds to the Feynman propagator on a compact bang-crunch universe. We present the connection matrix that relates past and future modes. We thoroughly discuss the physical implications of the antipodal map in both the Euclidean and Lorentzian geometries.
Highlights
Euclidean wormholes [1,2,3] are extrema of the Euclidean action whose interpretation is still partially shrouded in mystery
In this article we have reinterpreted euclidean wormholes as “holes of nothing”; after the antipodal map, the single exterior is that of flat space from which a sphere of size 2r1 has been excised
The solution is found to be stable under probe scalar perturbations
Summary
Euclidean wormholes [1,2,3] are extrema of the Euclidean action whose interpretation is still partially shrouded in mystery. They were proposed as a resolution to the cosmological constant problem [4], and as objects that lead to a loss of quantum coherence causing an inherent uncertainty in the fundamental constants of nature [2,5,6]. Whose few proposed resolutions suffer from closed timelike curves and other intricacies [10] Inspired by these questions, we study a Euclidean meron wormhole [11] in light of the antipodal Z2 mapping proposed by ’t Hooft. The analytic continuation of this solution results in a finite bang-crunch geometry [12], with temporal and spatial boundaries, opening up a possible handle on the problem of observables
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