Wave Optics in Gravitational Lensing

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.

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“…(22) coincides with the one derived under the geometrical optics. In geometrical optics, wave form is given by [11] …”

Section: B Geometrical Optics Limitmentioning

confidence: 99%

Exact wave propagation in a spacetime with a cosmic string

2006

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“…(14) using the saddle point method, as demonstrated in Ref. [15]. Using the approximate method, for w ≫ 1 and y ≪ 1/ √ w, we obtain µ(w, y) ≃ 2πwx…”

Section: Singular Isothermal Sphere Lensmentioning

confidence: 91%

“…For the case of multi-lensed images, in the geometrical optics approximation, the expression (18) means that the observed wave is described by a superposition of each wave with the amplitude, |µ( x j )| 1/2 , and the phase, wT ( x j , y) − (n j π)/2 [15].…”

Section: Geometrical Optics Approximationmentioning

confidence: 99%

The finite source size effect and wave optics in gravitational lensing

Matsunaga

Yamamoto

2006

J. Cosmol. Astropart. Phys.

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Abstract. We investigate the finite source size effect in the context of the wave optics in the gravitational lensing. The magnification of an extended source is presented in an analytic manner for the singular isothermal sphere lens model as well as the point mass lens model with the use of the thin lens approximation. The condition that the finite source size effect becomes substantial is demonstrated. As an application, we discuss possible observational consequences of the finite source size effect on astrophysical systems.

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“…We start by reviewing the path integral formalism for gravitational lens phenomenon [6]. We consider the Newtonian spacetime with the metric ( ) …”

Section: Generalized Formulationmentioning

confidence: 99%