Gravitationally induced interference of gravitational waves by a rotating massive object

Baraldo, Christian; Hosoya, Akio; Nakamura, T.

doi:10.1103/physrevd.59.083001

Cited by 52 publications

(54 citation statements)

References 21 publications

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“…(24) except for an overall phase e iroξ . This factor has been already absorbed in the choice of the normalization factor B in our formula (10).…”

Section: B Geometrical Optics Limitmentioning

confidence: 99%

“…More precisely, if the wavelength becomes comparable or longer than the Schwarzschild radius of the lens object, the diffraction effect becomes important and as a result the magnification factor approaches unity [1,2,3,4,5]. Mainly due to the possibility that the wave effects could be observed by future gravitational wave observations, several authors [6,7,8,9,10,11,12,13,14,15] have studied wave effects in gravitational lensing in recent years.…”

Section: Introductionmentioning

confidence: 99%

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Exact wave propagation in a spacetime with a cosmic string

2006

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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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“…(24) except for an overall phase e iroξ . This factor has been already absorbed in the choice of the normalization factor B in our formula (10).…”

Section: B Geometrical Optics Limitmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact wave propagation in a spacetime with a cosmic string

2006

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“…It must be interesting to study some models in detail. For instance, (1) how light curves change due to a Kerr lens?, (2) what changes occur in image positions and motions when a source is a binary star particularly a binary pulsar?, and (3) how images look like when a source is an accretion disk?…”

Section: Discussionmentioning

confidence: 99%

“…lens mass [2,3]. In other words, the Kerr lens would be equivalent to the Schwarzschild lens without any knowledge of the precise position of the lens [3].…”

mentioning

confidence: 99%

Separability of rotational effects on a gravitational lens

2003

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We derive the deflection angle up to O(m 2 a) due to a Kerr gravitational lens with mass m and specific angular momentum a. It is known that at the linear order in m and a the Kerr lens is observationally equivalent to the Schwarzschild one because of the invariance under the global translation of the center of the lens mass. We show, however, nonlinear couplings break the degeneracy so that the rotational effect becomes in principle separable for multiple images of a single source. Furthermore, it is distinguishable also for each image of an extended source and/or a point source in orbital motion.In practice, the correction at O(m 2 a) becomes O(10 −10 ) for the supermassive black hole in our galactic center. Hence, these nonlinear gravitational lensing effects are too small to detect by near-future observations. PACS Number(s); 95.30. Sf, 98.62.Sb, 04.70.Bw

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“…This subject is recently revisited by several authors, motivated by a possible phenomenon which might be observed in the future gravitational wave experiments [3][4][5][6][7][8][9][10][11][12]. In these works, the authors focus on the diffraction in the wave effect, which is substantial for λ ∼ R E , where λ is the wave length and R E is the Schwarzschild radius of the lens mass.…”

mentioning

confidence: 99%

Modulation of a chirp gravitational wave from a compact binary due to gravitational lensing

Yamamoto

2005

Phys. Rev. D

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A possible wave effect in the gravitational lensing phenomenon is discussed. We consider the interference of two coherent gravitational waves of slightly different frequencies from a compact binary, due to the gravitational lensing by a galaxy halo. This system shows the modulation of the wave amplitude. The lensing probability of such the phenomenon is of order 10 −5 for a high-z source, but it may be advantageous to the observation due to the magnification of the amplitude.The wave effect in gravitational lensing phenomenon has been investigated by many authors (see e.g., [1,2] and references therein). This subject is recently revisited by several authors, motivated by a possible phenomenon which might be observed in the future gravitational wave experiments [3][4][5][6][7][8][9][10][11][12]. In these works, the authors focus on the diffraction in the wave effect, which is substantial for λ ∼ R E , where λ is the wave length and R E is the Schwarzschild radius of the lens mass. However, in the present work, we focus on another different aspect of the wave effect, the modulation of superposed two waves, in the limit that the geometrical optics is valid λ ≪ R E . Some aspect of this effect has been investigated by the author and Tsunoda [13] as a lensing phenomenon by a cosmic string. Here we perform the similar analysis for the lensing by a galaxy halo. Throughout this paper, we use the convention G = c = 1.We start by considering the superposition of two lensed waves with the amplitude A 1 and A 2 and the angular frequencies ω 1 and ω 2 . Namely, we consider the wave expressed bywhere we assume that the phase δ involves the information of the path difference, and the difference of the frequencies ω 1 and ω 2 are due to the time delay effect. Assuming A 2 = A 1 + ∆A and ∆A << A 1 , E reduces toThis means that, if ∆A/A 1 ≪ 1, the wave amplitude modulates with the periodwhere ∆T is the time delay and dω/dt is the change rate of ω for an observer. We consider a gravitational wave from a binary of compact objects with equal mass M . By decreasing energy due to the gravitational wave radiation, the orbit of the binary changes. Thus the angular frequency ω changes. The rate of the change is estimated as [14],where z s is the redshift of the source. Here note that ω and t are the angular frequency and the time of the observer. Now we consider a lens halo modeled by the singular isothermal sphere with the velocity dispersion σ. Then the time delay is ∆T = 2.7 × 10where D OL , D OS and D LS are the angular diameter distances following the usual convention [2], f r is the flux ratio of the two waves, z l is the redshift of the lens, and we have adopted the Hubble parameter H 0 = 70km/s/Mpc. Then the period of the modulation is estimated as 1

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Gravitationally induced interference of gravitational waves by a rotating massive object

Cited by 52 publications

References 21 publications

Exact wave propagation in a spacetime with a cosmic string

Exact wave propagation in a spacetime with a cosmic string

Separability of rotational effects on a gravitational lens

Modulation of a chirp gravitational wave from a compact binary due to gravitational lensing

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