The Born approximation in wave optics gravitational lensing revisited
arXiv:2412.07272 · doi:10.1103/PhysRevD.111.083541
Abstract
The information about lensed gravitational waves is encapsulated by an amplification factor, which is calculated by an integration of an oscillatory function. The Born approximation, which has been studied in terms of wave optics in gravitational lensing, may provide a means of overcoming the difficulty in evaluating the oscillating function and better understanding the connection between the amplification factor and the lens mass distribution. In this paper, we revisit the Born approximation for a single lens plane. We find that the distortion of gravitational waves induced by wave optics gravitational lensing is in general connected with the mass distribution of the lens object through a convolution integral, where the scale of the kernel is determined by the Fresnel scale. We then study the validity and accuracy of the Born approximation specifically for the case of a point mass lens for which the exact analytical expression of the amplification factor is available. Using the dimensionless parameter , which represents the normalized impact parameter, and the dimensionless parameter , which denotes the normalized frequency, we show that the -th term of the Born approximation scales as . This indicates that, for the case of a point mass lens, the Born approximation is valid when is less than 1, with its accuracy scaling as in this regime.
arXiv comment9 pages, 5 figures, accepted for publication in Phys. Rev. D
References in corpus (23)
- Wave Effects in Gravitational Lensing of Gravitational Waves from Chirping Binaries
- Strong gravitational lensing of explosive transients
- Localizing merging black holes with sub-arcsecond precision using gravitational-wave lensing
- Probing Dark Low-mass Halos and Primordial Black Holes with Frequency-dependent Gravitational Lensing Dispersions of Gravitational Waves
- Femtolensing: Beyond the Semi-Classical Approximation
- The finite source size effect and the wave optics in gravitational lensing
- Gravitational wave lensing as a probe of halo properties and dark matter
- Probing the nature of dark matter via gravitational waves lensed by small dark matter halos
- Quasi-geometrical Optics Approximation in Gravitational Lensing
- Amplitude and Phase Fluctuations for Gravitational Waves Propagating through Inhomogeneous Mass Distribution in the Universe
- Small-scale shear: Peeling off diffuse subhalos with gravitational waves
- Scattering of Gravitational Waves by the Weak Gravitational Fields of Lens Objects
- Scattering of gravitational radiation: second order moments of the wave amplitude
- A Higher Probability of Detecting Lensed Supermassive Black Hole Binaries by LISA
- Weakly Lensed Gravitational Waves: Probing Cosmic Structures with Wave-Optics Features
- Convergence and Efficiency of Different Methods to Compute the Diffraction Integral for Gravitational Lensing of Gravitational Waves
- Wave propagation in a weak gravitational field and the validity of the thin lens approximation
- Amplitude and phase fluctuations of gravitational waves magnified by strong gravitational lensing
- Signatures of dark and baryonic structures on weakly lensed gravitational waves
- Weak lensing of gravitational waves in wave optics: Beyond the Born approximation
- Kramers-Kronig relation in gravitational lensing
- Universal relation between the variances of distortions of gravitational waves owing to gravitational lensing
- New Consistency Relations between Averages and Variances of Weakly Lensed Signals of Gravitational Waves