On a gravitational Aharonov–Bohm effect

Abstract

In this article we study the properties of certain quantum systems outside a rotating cosmic gauge string. It is shown that particle energies couple to the angular momentum density in the string, even though the particles are constrained only to move outside the string core where the Riemannian curvature vanishes identically. This effect may be looked upon as a gravitational analog of the Aharanov–Bohm effect. Due to the coupling of the particle energy to the angular momentum density in the string, it is shown that the angular momentum spectrum of the quantum particle is shifted by a constant amount. This, it is argued, will give rise to an nonvanishing angular momentum density in the quantum vacuum outside the rotating string. It is also shown that a quantum particle might experience an infinite blueshift in the presence of closed timelike curves outside such a string.

The magnetic field of a current carrying cosmic string

“…These and other astrophysical effects of a cosmic string are very well explained in a paper of Helliwell and Konkowski ͑1987͒. 12 Recently, a cylindrical metric was considered in another astrophysical application, out of the cosmic string context. 13 The authors considered the van Stockum metric, 14 which represents a dust distribution with rigid rotation around the symmetry axis, to model galaxies' jets.…”

Vacuum polarization on the spinning circle

“…Therefore the results in Ref. [5] are spoiled by improper use of T as a global time. [It should be mentioned that improper use of "helical times" as global times may also spoil results in other contexts.…”

“…The time coordinate T has been used in Ref. [5] to quantize a scalar field on the spinning circle. Although the background is flat, the corresponding two-point function presents (in addition to the usual flat divergence) short distance divergences containing the spin S as a factor.…”

“…Dy, 04.62.+v The study of quantum fields around cosmic strings is a pertinent issue since such defects may play a role in the cosmological scenario [1]. Most of the literature concerns spinless cosmic strings (see Ref.[1] and references therein), and only a few works have considered quantum mechanics and quantum field theory around spinning cosmic strings [2,3,4,5,6,7].The locally flat spacetime around an infinitely thin spinning cosmic string [1] is characterized by the line elementand by the identification (τ, ρ, ϕ, z) ∼ (τ, ρ, ϕ + 2π, z), where 0 < α ≤ 1 is the cone parameter and S ≥ 0 is the spin density (clearly the Minkowski spacetime corresponds to S = 0 and α = 1). As the region for which ρ < S/α contains closed timelike contours the spacetime is not globally hyperbolic.…”

“…[1] and references therein), and only a few works have considered quantum mechanics and quantum field theory around spinning cosmic strings [2,3,4,5,6,7].…”