Exact Wave Propagation in a Spacetime with a Cosmic String

We present exact solutions of the massless Klein-Gordon equation in a spacetime in which an infinite straight cosmic string resides. The first solution represents a plane wave entering perpendicular to the string direction. We also present and analyze a solution with a static point-like source. In the short wavelength limit these solutions approach the results obtained by using the geometrical optics approximation: magnification occurs if the observer lies in front of the string within a strip of angular width 8πGμ, where μ is the string tension. We find that when the distance from the observer to the string is less than 10−3(Gμ)−2 λ ∼ 150Mpc(λ/AU)(Gμ/10−8)−2 where λ is the wave length, the magnification is significantly reduced compared with the estimate based on the geometrical optics due to the diffraction effect.