We reexamine the light deflection by an Ellis wormhole. The bending angle as a function of the ratio between the impact parameter and the throat radius of the wormhole is obtained in terms of a complete elliptic integral of the first kind. This result immediately yields asymptotic expressions in the weak field approximation. It is shown that an expression for the deflection angle derived (and used) in recent papers is valid at the leading order but it breaks down at the next order because of the nontrivial spacetime topology.PACS numbers: 95.30.Sf, 98.62.Sb
We examine a gravitational lens model inspired by modified gravity theories and exotic matter and energy. We study an asymptotically flat, static, and spherically symmetric spacetime that is modified in such a way that the spacetime metric depends on the inverse distance to the power of positive n in the weak-field approximation. It is shown analytically and numerically that there is a lower limit on the source angular displacement from the lens object to get demagnification.Demagnifying gravitational lenses could appear, provided the source position β and the power n satisfy β > 2/(n + 1) in the units of the Einstein ring radius under a large-n approximation.Unusually, the total amplification of the lensed images, though they are caused by the gravitational pull, could be less than unity. Therefore, time-symmetric demagnification parts in numerical light curves by gravitational microlensing (F.Abe, Astrophys. J. 725, 787, 2010) may be evidence of an Ellis wormhole (being an example of traversable wormholes), but they do not always prove it.Such a gravitational demagnification of the light might be used for hunting a clue of exotic matter and energy that are described by an equation of state more general than the Ellis wormhole case.Numerical calculations for the n = 3 and 10 cases show maximally ∼ 10 and ∼ 60 percent depletion of the light, when the source position is β ∼ 1.1 and β ∼ 0.7, respectively. PACS numbers: 95.30.Sf, 98.62.Sb
Gravitational lens models with negative convergence (surface mass density projected onto the lens plane) inspired by modified gravity theories, exotic matter and energy have been recently discussed in such a way that a static and spherically-symmetric modified spacetime metric depends on the inverse distance to the power of positive n (n=1 for Schwarzschild metric, n=2 for Ellis wormhole) in the weak-field approximation [Kitamura, Nakajima and Asada, PRD 87, 027501 (2013)], and it has been shown that demagnification of images could occur for n > 1 lens models associated with exotic matter (and energy), though they cause the gravitational pull on light rays. The present paper considers gravitational lensing shear by the demagnifying lens models and other models such as negative-mass compact objects causing the gravitational repulsion on light rays like a concave lens. It is shown that images by the lens models for the gravitational pull are tangentially elongated, whereas those by the repulsive ones are radially distorted. This feature of lensed image shapes may be used for searching (or constraining) localized exotic matter or energy with gravitational lensing surveys. It is suggested also that an underdense region such as a cosmic void might produce radially elongated images of background galaxies rather than tangential ones. 95.30.Sf, 98.62.Sb
Gravitational lens models, some of which might act as if a concave lens, have been recently investigated by using a static and spherically symmetric modified spacetime metric that depends on the inverse distance to the $n$-th power [Kitamura, Nakajima and Asada, PRD 87, 027501 (2013)]. We reexamine the time delay of light in a gravitational concave lens as well as a gravitational convex one. The frequency shift due to the time delay is also investigated. We show that the sign of the time delay in the lens models is the same as that of the deflection angle of light. The size of the time delay decreases with increase in the parameter $n$. We discuss also possible parameter ranges that are relevant to pulsar timing measurements in our galaxy.Comment: 16 pages, 7 figures. arXiv admin note: text overlap with arXiv:1307.663
The gravitational lensing effects in the weak gravitational field by exotic lenses have been investigated intensively to find nonluminous exotic objects. Gravitational lensing based on 1/r n fall-off metric, as a one-parameter model that can treat by hand both the Schwarzschild lens (n=1) and the Ellis wormhole (n=2) in the weak field, has been recently studied. Only for n = 1 case, however, it has been explicitly shown that effects of relativistic lens images by the strong field on the light curve can be neglected. We discuss whether relativistic images by the strong field can be neglected for n > 1 in the Tangherlini spacetime which is one of the simplest models for our purpose. We calculate the divergent part of the deflection angle for arbitrary n and the regular part for n = 1, 2 and 4 in the strong field limit, the deflection angle for arbitrary n under the weak gravitational approximation. We also compare the radius of the Einstein ring with the radii of the relativistic Einstein rings for arbitrary n. We conclude that the images in the strong gravitational field have little effect on the total light curve and that the time-symmetric demagnification parts in the light curve will appear even after taking account of the images in the strong gravitational field for n > 1.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.