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 $8\pi G\mu$, where $\mu$ is the string tension. We find that when the distance from the observer to the string is less than $10^{-3}{(G\mu )}^{-2}\lambda \sim 150\mathrm{Mpc}(\lambda /\mathrm{AU})(G\mu /10^{-8}{)}^{-2}$, where $\lambda$ 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.

15 pages, 8 figures, reference added

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• Lensing of gravitational waves: universal signatures in the beating pattern
• Diffraction of light by topological defects in liquid crystals
• Emergence of Fresnel diffraction zones in gravitational lensing by a cosmic string
• Spin wave optics for gravitational waves lensed by a Kerr black hole
• Wave propagation in metamaterials mimicking the topology of a cosmic string
• Compact Binaries through a Lens: Silent vs. Detectable Microlensing for the LIGO-Virgo-KAGRA Gravitational Wave Observatories
• Wave diffraction by a cosmic string
• Probing Cosmic Strings with Gravitational-Wave Fringe
• Parameter estimation of microlensed gravitational waves with Conditional Variational Autoencoders
• Femto-lensing due to a Cosmic String
• Probing cosmic strings via gravitational-wave lensing