Optics in the Schwarzschild spacetime

Čadež, A.; Kostić, U.

doi:10.1103/physrevd.72.104024

Cited by 38 publications

(42 citation statements)

References 24 publications

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“…Our main result is the explicit computation of the two possible time transfer functions T + and T − relative to the optical metric (8). The expressions of these functions yielded by Eq.…”

Section: Discussionmentioning

confidence: 99%

“…These light rays are regarded as exact solutions to the null geodesics equations of the metric (8). This means that we do not assume from the beginning that the solutions can be represented as power series in m. However, restricting to a linearized metric implies that only the light rays confined in regions of spacetime such that r ≫ m can be considered as relevant in the present analysis.…”

Section: Generalitiesmentioning

confidence: 99%

“…(13) passing through two given points x A and x B and having their concavity oriented toward the origin, provided that x A and x B are not aligned with O. Consequently, there exist two and only two time transfer functions in the background defined by the optical metric (8). Of course, the time transfer functions coincide when x A and x B are aligned with O.…”

Section: Nonradial Null Geodesicsmentioning

confidence: 99%

“…Even for the Schwarzschild metric in which the exact solutions to the geodesic equations are known (see, e.g., [7] and Refs. therein), the null geodesics passing through two given points are only determined in an implicit, very hard to work manner [8].…”

Section: Introductionmentioning

confidence: 99%

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Time transfer functions in Schwarzschild-like metrics in the weak-field limit: A unified description of Shapiro and lensing effects

Linet

Teyssandier

2016

Phys. Rev. D

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We present a complete analysis of the light rays within the linearized, weak-field approximation of a Schwarzschild-like metric describing the gravitational field of an isolated, spherically symmetric body. We prove in this context the existence of two time transfer functions and we obtain these functions in an exact closed-form. We are led to distinguish two regimes. In the first regime, the two time transfer functions correspond to rays which are confined in regions of spacetime where the weak-field approximation is valid. Such a regime occurs in gravitational lensing configurations with double images of a given source. We find the general expressions of the angular separation and the difference in light travel time between the two images. In the second regime, there exists only one time transfer function corresponding to a light ray remaining in a region of weak field. Performing a Taylor expansion of this function with respect to the gravitational constant, we obtain the Shapiro time delay completed by a series of so-called "enhanced terms." The enhanced terms beyond the third order are new. PACS numbers: 04.25.-g, 04.80. Cc, 95.10.Jk, 95.30.Sf

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“…Our main result is the explicit computation of the two possible time transfer functions T + and T − relative to the optical metric (8). The expressions of these functions yielded by Eq.…”

Section: Discussionmentioning

confidence: 99%

Section: Generalitiesmentioning

confidence: 99%

Section: Nonradial Null Geodesicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Time transfer functions in Schwarzschild-like metrics in the weak-field limit: A unified description of Shapiro and lensing effects

Linet

Teyssandier

2016

Phys. Rev. D

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“…After this moment, pressure forces become negligible with respect to inertial forces and the particles that constitute the object start to fall freely in the gravitational field of the black hole. A ray-tracing procedure [14] from points on the object's surface to the distant observer is used to determine its appearance and light curve. The resulting light curves are then used to fit an observed X-ray flare from Sgra A * .…”

Section: Tidal Disruption and X-ray Flaresmentioning

confidence: 99%

Tidal disruption of asteroids by supermassive black holes

Kostić

Čadež

Calvani

et al. 2012

EPJ Web of Conferences

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Abstract. The compact radio source Sgr A * at the centre of our Galaxy harbours a super-massive black hole, and is therefore the nearest laboratory for testing the super-massive black hole astrophysics and environment. Since it is not an active galactic nucleus, it also offers the possibility of observing the capture of low-mass objects, such as comets or asteroids, that may orbit the central black hole. In this paper we discuss conditions for tidal disruption of low-mass objects and predictions of the appearance and light curve of such events, as well as their relevance for the X-ray and infra-red flares detected in Sgr A * . The modelled light curves of such tidal disruption events bear marks of the strong gravitational field: tidal squeezing and elongation of the object, gravitational lensing, aberration of light, and Doppler effects. Finally, we show that this model is able to reproduce and fit X-ray flares.

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Boblest

Müller

2022

Spezielle Und Allgemeine Relativitätstheorie

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Optics in the Schwarzschild spacetime

Cited by 38 publications

References 24 publications

Time transfer functions in Schwarzschild-like metrics in the weak-field limit: A unified description of Shapiro and lensing effects

Time transfer functions in Schwarzschild-like metrics in the weak-field limit: A unified description of Shapiro and lensing effects

Tidal disruption of asteroids by supermassive black holes

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