Wave diffraction by a cosmic string

Abstract

We show that if a cosmic string exists, it may be identified through characteristic diffraction pattern in the energy spectrum of the observed signal. In particular, if the string is on the line of sight, the wave field is shown to fit the Cornu spiral. We suggest a simple procedure, based on Keller's geometrical theory of diffraction, which allows to explain wave effects in conical spacetime of a cosmic string in terms of interference of four characteristic rays. Our results are supposed to be valid for scalar massless waves, including gravitational waves, electromagnetic waves, or even sound in case of condensed matter systems with analogous topological defects.Comment: 5 pages, 6 figures; free access to journal version until September 20, 2016 at http://authors.elsevier.com/a/1TTdX1LUy9BfY

Emergence of Fresnel diffraction zones in gravitational lensing by a cosmic string

“…Taking into account that 0 ≤ ∆ ≤ π/2, it can be seen that γ only ranges from 1 to √ 2. In the plane-wave limit, r 0 → ∞, one gets γ → 1 and recovers the result of our previous work [5]: F = 2 e −iψ F( √ ψ). A simpler formula can be obtained by expanding the Fresnel integral F in Eq.…”

“…Second, we take into account the curvature of the incident wavefront by considering the wave source at a finite distance from the string. This is a more general case with respect to our previous study [5]. By applying the uniform asymptotic theory of diffraction [12,13], we obtain analytical solutions for the wave field in the whole space including the lines of singularities at the boundaries of the double-imaging region.…”

“…This scaling cannot be applied to a string, a non-compact object with conical topology. It has been shown recently for the plane-wave diffraction by string [5] that the Fresnel number is determined by the ratio r∆ 2 /λ, where r is the distance from the string to the observer and ∆ is a constant related to the deficit angle of conical space, which is proportional to the linear mass of the string [6][7][8]. For the typical ∆ ∼ 10 −7 , low Fresnel numbers can be achieved at cosmological distances from the string, r ∼ 10 14 λ.…”

Wave propagation in metamaterials mimicking the topology of a cosmic string

“…which is precisely the equation used in Refs. [31][32][33][34] for the cosmic string background (4).…”

“…The physical interpretaion of the D waves is the following: they are the waves that go from the source to an observer but hitting the string, following the shortest path [33,34].…”