In this paper we investigate the relation between the potential and geometric time delays in gravitational lensing. In the original paper of Shapiro (1964), it is stated that there is a time delay in the radar signals between Earth and Venus that pass near a massive object (the Sun), compared to the path taken in the absence of any mass. The reason for this delay is connected with the influence of gravity on the coordinate velocity of a light ray in a gravitational potential. The contribution from the change of the path length, which happens to be of second order, is considered as negligible. Nevertheless, in the gravitational lens theory the geometrical delay, related to the change of path length, is routinely taken into account along with the potential term. In this work we explain this apparent discrepancy. We address the contribution of the geometric part of the time delay in different situations, and introduce a unified treatment with two limiting regimes of lensing. One of these limits corresponds to the time delay experiments near the Sun where the geometrical delay is shown to be negligible. The second corresponds to the typical gravitational lens scenario with multiple imaging where the geometrical delay is shown to be significant. We introduce a compact, analytical, and quantitative criteria based on relation between the angular position of source and the Einstein radius. This criterion allows one to find out easily when it is necessary to take the geometrical delay into account. In particular, it is shown that the geometrical delay is non-negligible in the case of good alignment between source, lens and observer, because in such a case it becomes a first order quantity (the same order as the potential term).
When gravitational waves propagate near massive objects, their paths curve resulting in gravitational lensing, which is expected to be a promising new instrument in astrophysics. If the time delay between different paths is comparable with the wave period, lensing may induce beating patterns in the waveform, and it is very close to caustics that these effects are likely to be observable. Near the caustic, however, the short-wave asymptotics associated with the geometrical optics approximation breaks down. In order to describe properly the crossover from wave optics to geometrical optics regime…
A geometrical-optics analogy for gravitational lensing using axicon-type lenses
Institut für Astronomie und Astrophysik, Eberhard Karls Universität Tübingen（蒂宾根大学天文与天体物理研究所）；Department of Optics, Faculty of Physical Sciences, Universidad Complutense de Madrid（马德里康普顿斯大学物理科学学院光学系）
Gravitational Light Deflection: Geometrical Methods and Nonlinear Electrodynamics
M. P, Birla Institute of Fundamental Research（Birla基础研究所）；Saha Institute of Nuclear Physics（萨哈核物理研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Indian Statistical Institute（印度统计研究所）；Department of Physics, Jhargram Raj College（Jhargram皇家学院物理系）
It is known that geometrical optics no longer applies to the gravitational lensing if the wavelength of a propagating wave becomes comparable to or larger than the Schwarzshild radius of a lensing object. We investigate the propagation of gravitational waves in wave optics, particularly focusing on the difference between their arrival time and the arrival time of light. We argue that, contrary to the observation in the previous work, gravitational waves never arrive at an observer earlier than light when both gravitational waves and light are emitted from a same source simultaneously.
Gravitational waves are theorized to be gravitationally lensed when they propagate near massive objects. Such lensing effects cause potentially detectable repeated gravitational wave patterns in ground- and space-based gravitational wave detectors. These effects are difficult to discriminate when the lens is small and the repeated patterns superpose. Traditionally, matched filtering techniques are used to identify gravitational-wave signals, but we instead aim to utilize machine learning techniques to achieve this. In this work, we implement supervised machine learning classifiers (support vec…
In this paper, we study the strong gravitational lensing of gravitational waves (GWs) from a statistical perspective, with particular focus on the high frequency GWs from stellar binary black hole coalescences. These are most promising targets for ground-based detectors such as Advanced Laser Interferometer Gravitational Wave Observatory (aLIGO) and the proposed Einstein Telescope (ET) and can be safely treated under the geometrical optics limit for GW propagation. We perform a thorough calculation of the lensing rate, by taking account of effects caused by the ellipticity of lensing galaxies,…
Plasma impact on black hole shadow and gravitational weak lensing for Schwarzschild-like black hole
Harbin Institute of Technology（哈尔滨工业大学）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；New Uzbekistan University（新乌兹别克斯坦大学）；National University of Uzbekistan（乌兹别克斯坦国立大学）
We present a new idea of testing the validity of the Friedman-Lema\^ıtre-Robertson-Walker metric, through the multiple measurements of galactic-scale strong gravitational lensing systems with type Ia supernovae in the role of sources. Each individual lensing system will provide a model-independent measurement of the spatial curvature parameter referring only to geometrical optics independently of the matter content of the universe. This will create a valuable opportunity to test the FLRW metric directly. Our results show that with hundreds of strongly lensed SNe Ia observed by LSST, one would …
In this paper, we study the weak deflection angle of black hole in effective loop quantum gravity using the geometrical technique used by Gibbons and Werner. We first derive the optical metric, calculate the Gaussian optical curvature, and then apply the Gauss-Bonnet theorem. We then also investigate the effect of plasma and dark matter mediums on the weak deflection angle. We show that increasing the impact of these two mediums grows the deflection angle. We also calculate the Hawking temperature via Gauss-Bonnet theorem. In addition, we determine the fermionic greybody bounds. Moreover, we d…
