A formula to investigate the wave effect in a multi-lens system is presented on the basis of a path integral formalism by generalizing the work by Nakamura and Deguchi (1999). The wave effect of a system with two lenses is investigated in an analytic way as a simple application to demonstrate usefulness of the formula and variety of wave effect in multi-lens system.
References
[1]
Takahashi, R. and Nakamura, T. (2003) Wave Effects in the Gravitational Lensing of Gravitational Waves from Chirping Binaries. The Astrophysical Journal, 595, 1039-1051. https://doi.org/10.1086/377430
[2]
Seto, N. (2004) Strong Gravitational Lensing and Localization of Merging Massive Black Hole Binaries with LISA. Physical Review D, 69, Article ID: 022002 https://doi.org/10.1103/PhysRevD.69.022002
[3]
Yamamoto, K. and Tsunoda, K. (2003) Wave Effect in Gravitational Lensing by a Cosmic String. Physical Review D, 68, Article ID: 041302. https://doi.org/10.1103/PhysRevD.68.041302
[4]
De Paolis, F., Ingrosso, G., Nucita, A.A. and Qadir, A. (2002) A Note on Gravitational Wave Lensing. Astronomy and Astrophysics, 394, 749-752. https://doi.org/10.1051/0004-6361:20021258
[5]
Baraldo, C., Hosoya, A. and Nakamura, T.T. (1999) Gravitationally Induced Interference of Gravitational Waves by a Rotating Massive Object. Physical Review D, 59, Article ID: 083001. https://doi.org/10.1103/PhysRevD.59.083001
[6]
Nakamura, T.T. and Deguchi, S. (1999) Wave Optics in Gravitational Lensing. Progress of Theoretical Physics Supplement, 133, 137-153. https://doi.org/10.1143/PTPS.133.137
[7]
Nakamura, T.T. (1998) Gravitational Lensing of Gravitational Waves from Inspiraling Binaries by a Point Mass Lens. Physical Review Letters, 80, 1138-1141. https://doi.org/10.1103/PhysRevLett.80.1138
[8]
Deguchi, S. and Watson, W.D. (1986) Wave Effects in Gravitational Lensing of Electromagnetic Radiation. Physical Review D (Particles and Fields), 34, 1708-1718. https://doi.org/10.1103/PhysRevD.34.1708
[9]
Deguchi, S. and Watson, W.D. (1986) Diffraction in Gravitational Lensing for Compact Objects of Low Mass. Astrophysical Journal, Part 1, 307, 30-37. https://doi.org/10.1086/164389
[10]
Schneider, P., Ehlers, J. and Falco, E.E. (1992) Gravitational Lenses. Springer-Verlag, Berlin.
[11]
Magnus, W., Oberhettinger, F. and Soni, R.P. (1966) Formulas and Theorems for the Special Functions of Mathematical Physics. Springer-Verlag, Berlin. https://doi.org/10.1007/978-3-662-11761-3
