Spacetime perspective of Schwarzschild lensing

We calculate the time delay between different relativistic images formed by black hole gravitational lensing in the strong field limit. For spherically symmetric black holes, it turns out that the time delay between the first two images is proportional to the minimum impact angle. Their ratio gives a very interesting and precise measure of the distance of the black hole. Moreover, using also the separation between the images and their luminosity ratio, it is possible to extract the mass of the black hole. The time delay for the black hole at the center of our Galaxy is just few minutes, but for supermassive black holes with M = 10 8 ÷ 10 9 M⊙ in the neighbourhood of the Local Group the time delay amounts to few days, thus being measurable with a good accuracy.

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“…(8). Of course, dt/dx tends to one for large x and the two integrals in (28) are separately divergent, while their difference is finite.…”

Section: Time Delay In the Strong Field Limitmentioning

confidence: 99%

“…In this way, a set of infinite relativistic images can be generated on each side of the black hole [3,4]. Several approaches have been proposed to study gravitational lensing in the strong field limit [4,5,6,7,8,9,10], while Falcke, Melia & Agol, in a different perspective, studied the accretion flow as a source [11]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Time Delay in Black Hole Gravitational Lensing as a Distance Estimator

Bozza

Mancini

2004

General Relativity and Gravitation

114

171

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“…Detailed discussions on limit (SDL)), has received wide attention in the recent past. The development of lensing theory in the strong-field regime started with the work of Frittelli, Kling and Newman [15] and that of Virbhadra and Ellis [16]. These authors proposed a definition of an exact lens equation without reference to background spacetime, and constructed the exact lens equation explicitly in the case of the Schwarzschild spacetime.…”

Section: Introductionmentioning

confidence: 99%

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

Gyulchev

Yazadjiev

2007

Phys. Rev. D

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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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“…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%

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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Spacetime perspective of Schwarzschild lensing

Cited by 243 publications

References 8 publications

Time Delay in Black Hole Gravitational Lensing as a Distance Estimator

Time Delay in Black Hole Gravitational Lensing as a Distance Estimator

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

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

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