Orbits of massless particles in the Schwarzschild metric: Exact solutions

Muñoz, Gerardo

doi:10.1119/1.4866274

Cited by 26 publications

(21 citation statements)

References 13 publications

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“…This work introduces a family of two distinct exponential solutions which together provide a succinct description of the entire orbital trajectories of light near a Schwarzschild black hole. Thereby we provide analytical insight into the solutions previously developed 2,[4][5][6][7][8] . Our formalism provides a few important interpretations.…”

Section: Discussionmentioning

confidence: 95%

“…Therefore, the observer will see the entire surface of the event horizon and the entire universe repeating infinitely near the edges of the black hole. This infinite mapping has been extensively studied with the deflection angle diverging logarithmically in the strong field limit 2,[4][5][6][7][8] .…”

Section: Divergent Reflections Around the Photon Sphere Of A Black Hole Albert Snepppenmentioning

confidence: 99%

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Divergent reflections around the photon sphere of a black hole

Sneppen

2021

Sci Rep

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From any location outside the event horizon of a black hole there are an infinite number of trajectories for light to an observer. Each of these paths differ in the number of orbits revolved around the black hole and in their proximity to the last photon orbit. With simple numerical and a perturbed analytical solution to the null-geodesic equation of the Schwarzschild black hole we will reaffirm how each additional orbit is a factor $$e^{2 \pi }$$ e 2 π closer to the black hole’s optical edge. Consequently, the surface of the black hole and any background light will be mirrored infinitely in exponentially thinner slices around the last photon orbit. Furthermore, the introduced formalism proves how the entire trajectories of light in the strong field limit is prescribed by a diverging and a converging exponential. Lastly, the existence of the exponential family is generalized to the equatorial plane of the Kerr black hole with the exponentials dependence on spin derived. Thereby, proving that the distance between subsequent images increases and decreases for respectively retrograde and prograde images. In the limit of an extremely rotating Kerr black hole no logarithmic divergence exists for prograde trajectories.

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Section: Discussionmentioning

confidence: 95%

Section: Divergent Reflections Around the Photon Sphere Of A Black Hole Albert Snepppenmentioning

confidence: 99%

Divergent reflections around the photon sphere of a black hole

Sneppen

2021

Sci Rep

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“…With η = 0, we arrive ar r ph = 3r s /2, which is the location of photon orbit in Schwarzschild BH [52,53]. In Fig.…”

Section: The Scalar Field Equation Of Motionmentioning

confidence: 99%

Thermal behavior of a radially deformed black hole spacetime

Barman

Mukherjee

2021

Eur. Phys. J. C

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In the present article, we study the Hawking effect and the bounds on greybody factor in a spacetime with radial deformation. This deformation is expected to carry the imprint of a non-Einsteinian theory of gravity, but shares some of the important characteristics of general relativity (GR). In particular, this radial deformation will restore the asymptotic behavior, and also allows for the separation of the scalar field equation in terms of the angular and radial coordinates – making it suitable to study the Hawking effect and greybody factors. However, the radial deformation would introduce a change in the locations of the horizon, and therefore, the temperature of the Hawking effect naturally alters. In fact, we observe that the deformation parameter has an enhancing effect on both temperature and bounds on the greybody factor, which introduces a useful distinction with the Kerr spacetime. We discuss these effects elaborately, and broadly study the thermal behavior of a radially deformed spacetime.

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“…Due to their strong gravitational field, the higher-order PN effects caused by the black holes on the passing-by light might be detected in future. The light propagation in the field of Schwarzschild black hole has been studied extensively [22][23][24][25][26][27]. For the case of Kerr black hole, the trajectory of the light is not confined to a plane in general, except for the light being in the equatorial plane which is the perpendicular to the gravitational source's rotational axis.…”

Section: Introductionmentioning

confidence: 99%

Post-Newtonian light propagation in Kerr-Newman spacetime

Jiang

Lin

2018

Phys. Rev. D

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The second-order post-Newtonian solution for the light propagation in the field of Kerr-Newman black hole is achieved via an iterative method. Based on this result, we further obtain the secondorder post-Newtonian light deflection in Kerr-Newman spacetime, which is formulated in an united form for any arbitrarily incident directions. All results are exhibited in the coordinate system constituted by the initial light-direction vector, the impact vector, and their cross-product.

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Orbits of massless particles in the Schwarzschild metric: Exact solutions

Cited by 26 publications

References 13 publications

Divergent reflections around the photon sphere of a black hole

Divergent reflections around the photon sphere of a black hole

Thermal behavior of a radially deformed black hole spacetime

Post-Newtonian light propagation in Kerr-Newman spacetime

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