Exact Wave Propagation in a Spacetime with a Cosmic String

Abstract

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} {(G μ)}^{-2}λ\sim 150 {\rm Mpc} (λ/{\rm 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. For gravitational waves from neutron star(NS)-NS mergers the several lensing events per year may be detected by DECIGO/BBO.