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 (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. For gravitational waves from neutron star(NS)-NS mergers the several lensing events per year may be detected by DECIGO/BBO.

Arrival Time Differences Between Gravitational Waves and Electromagnetic Signals Due to Gravitational Lensing

“…Nakamura (1998) discussed the diffraction effect on lensing magnifications for inspiraling binaries induced by intervening compact objects. Wave effects in the gravitational lensing of GWs have been discussed linked to several topics (e.g., Baraldo et al 1999;Takahashi & Nakamura 2003;Takahashi 2004;Takahashi et al 2005;Suyama et al 2005Suyama et al , 2006Yoo et al 2007;Sereno et al 2010;Yoo et al 2013;Cao et al 2014). Figure 1 shows a lensing configuration with an observer, a lens, and a source in a nearly straight line.…”

Wave diffraction by a cosmic string

“…Next, unlike Ref. [17], we perform the coordinate transformation taking advantage of the flat background (2). To do that, we place the cut line SA strictly perpendicular to the wavefront of the incident wave, as shown in Fig.…”

“…The images should be undistorted but they may overlap if the split angle, which is proportional to the string tension, is small. In such a case, the wave effects are extremely important as a probe in gravitational lensing [12], that was extensively studied for compact or point-like objects [13], but only a few studies are known for the strings [14][15][16][17][18].…”

Wave effect in gravitational lensing by the Ellis wormhole

“…The source must be compact enough to show the clear oscillation behaviour in the spectrum. This fact can be clearly understood by considering the y dependence of the phase in the amplification factor (33). Since τ (y) is roughly approximated by 2y, the period δy for one cycle is given by δy ∼ π/(ωd).…”

“…[28,29]. Wave effects in gravitational lensing by the rotating massive object [30], binary system [31], singular isothermal sphere [32] and the cosmic string [33,34] have been considered. In Sec.…”