Exact gravitational lens equation in spherically symmetric and static spacetimes

Perlick, Volker

doi:10.1103/physrevd.69.064017

Cited by 252 publications

(259 citation statements)

References 32 publications

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“…In order to understand a strong gravitational field, a more rigorous formulation of the bending angle has been investigated [8][9][10][11][12][13][14][15]. For instance, strong-field gravitational lensing in a Schwarzschild black hole was investigated by Frittelli, Kling and Newman [8], by Virbhadra and Ellis [9] and more comprehensively by Virbhadra [10]; distinctive lensing features of naked singularities were studied by many authors [11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

“…For instance, strong-field gravitational lensing in a Schwarzschild black hole was investigated by Frittelli, Kling and Newman [8], by Virbhadra and Ellis [9] and more comprehensively by Virbhadra [10]; distinctive lensing features of naked singularities were studied by many authors [11][12][13][14][15][16][17][18][19][20]. Kitamura, Nakajima and Asada proposed a lens model in the inverse powers of the distance as 1/r n [21], such that the Schwarzschild lens, the Ellis wormhole lens and a gravitational lens associated with exotic matter (or energy) that might follow a non-standard equation of state can be discussed in a unified manner of describing these models as a one parameter family [22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

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Finite-distance corrections to the gravitational bending angle of light in the strong deflection limit

et al. 2017

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Continuing work initiated in an earlier publication [Ishihara, Suzuki, Ono, Kitamura, Asada, Phys. Rev. D 94, 084015 (2016) ], we discuss a method of calculating the bending angle of light in a static, spherically symmetric and asymptotically flat spacetime, especially by taking account of the finite distance from a lens object to a light source and a receiver. For this purpose, we use the Gauss-Bonnet theorem to define the bending angle of light, such that the definition can be valid also in the strong deflection limit. Finally, this method is applied to Schwarzschild spacetime in order to discuss also possible observational implications. The proposed corrections for Sgr A * for instance are able to amount to ∼ 10 −5 arcseconds for some parameter range, which may be within the capability of near-future astronomy, while also the correction for the Sun in the weak field limit is ∼ 10 −5 arcseconds. 95.30.Sf, 98.62.Sb

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finite-distance corrections to the gravitational bending angle of light in the strong deflection limit

et al. 2017

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“…The visualization of the Ellis wormhole was studied by Muller [59]. The gravitational lenses of a source on the other side of the Ellis wormhole were investigated by Perlick [60] and Tsukamoto and Harada [61].…”

Section: Introductionmentioning

confidence: 99%

Strong deflection limit analysis and gravitational lensing of an Ellis wormhole

Tsukamoto

2016

Phys. Rev. D

151

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Observations of gravitational lenses in strong gravitational fields give us a clue to understanding dark compact objects. In this paper, we extend a method to obtain a deflection angle in a strong deflection limit provided by Bozza [Phys. Rev. D 66, 103001 (2002)] to apply to ultrastatic spacetimes. We also discuss on the order of an error term in the deflection angle. Using the improved method, we consider gravitational lensing by an Ellis wormhole, which is an ultrastatic wormhole of the Morris-Thorne class.

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“…After this paper Virbhadra and Ellis [17] numerically investigated the lensing by naked singularities. On the other hand, Perlick [18] has considered lensing in a spherically symmetric and static spacetime, based on the lightlike geodesic equation without approximations. Eiroa, Romero and Torres [19] have described Reissner-Nordstrom black hole lensing, confirming the appearance of a similar patterns of images.…”

Section: Introductionmentioning

confidence: 99%

Kerr-Sen dilaton-axion black hole lensing in the strong deflection limit

2007

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In the present work we study numerically quasi-equatorial lensing by the charged, stationary, axially-symmetric Kerr-Sen dilaton-axion black hole in the strong deflection limit. In this approximation we compute the magnification and the positions of the relativistic images. The most outstanding effect is that the Kerr-Sen black hole caustics drift away from the optical axis and shift in clockwise direction with respect to the Kerr caustics. The intersections of the critical curves on the equatorial plane as a function of the black hole angular momentum are found, and it is shown that they decrease with the increase of the parameter Q 2 /M . All of the lensing quantities are compared to particular cases as Schwarzschild, Kerr and Gibbons-Maeda black holes. I. INTRODUCTIONOne of the consequences of Einstein's General Theory of Relativity is that light rays are deflected by gravity. Although this discovery was made in the last century, the possibility that there could be such a deflection had been suspected much earlier, by Newton and Laplace, for the first time. The phenomena resulting from the deflection of electromagnetic radiation in a gravitational field are referred to as gravitational lensing (GL) and an object causing a detectable deflection is known as a gravitational lens. Nowadays, gravitational lensing is a rapidly developing area of research, and it has found applications ranging from the search of extrasolar planets and compact dark matter to the estimation of the values of the cosmological parameters [10]. In most of these cases it is possible to assume that the gravitational field is weak, hence the angle of deflection of the light in the field of a spherically symmetric body with mass M can be approximated by: that the present lens model could be able to distinguish observationally a black hole from naked singularity.The study of the gravitational lensing when light passes very close to a massive body, such as a black hole (a process also known as gravitational lensing in the strong deflection

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Exact gravitational lens equation in spherically symmetric and static spacetimes

Cited by 252 publications

References 32 publications

Finite-distance corrections to the gravitational bending angle of light in the strong deflection limit

Finite-distance corrections to the gravitational bending angle of light in the strong deflection limit

Strong deflection limit analysis and gravitational lensing of an Ellis wormhole

Kerr-Sen dilaton-axion black hole lensing in the strong deflection limit

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