Exact formulas for spherical photon orbits around Kerr black holes

Tavlayan, Aydin; Tekin, Bayram

doi:10.1103/physrevd.102.104036

Cited by 19 publications

(21 citation statements)

References 18 publications

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“…There is a third constant of motion κ, called Carter constant [35], which is related with a symmetric rank two Killing tensor and determines the behavior of the photon's motion in the θ-direction [25]. κ = 0 characterizes the equatorial motion of photon [31,32]. A relevant property of the Carter constant is κ 0 [31,32].…”

Section: Null Geodesics Around Kerr-newman Black Holesmentioning

confidence: 99%

“…κ = 0 characterizes the equatorial motion of photon [31,32]. A relevant property of the Carter constant is κ 0 [31,32]. Using the above mentioned three constants of motion, the geodesic motion of the photon around the Kerr-Newman black hole is governed by the following set of first-order differential equations (we define a new variable o ≡ cos θ in place of the coordinate θ)…”

Section: Null Geodesics Around Kerr-newman Black Holesmentioning

confidence: 99%

“…The radii of the photon orbits are analytically found for the case with the critical inclination angle. For the case with a generic inclination angle, approximate analytical expressions of the radii are provided [32].…”

Section: Introductionmentioning

confidence: 99%

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Radii of spherical photon orbits around Kerr-Newman black holes

Chen¹,

Huang²,

Jiang³

2022

Preprint

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The spherical photon orbits around a black hole with constant radii are particular important in astrophysical observations of the black hole. In this paper, the equatorial and non-equatorial spherical photon orbits around Kerr-Newman black holes are studied. The radii of these orbits satisfy a sextic polynomial equation with three parameters, the rotation parameter u, charge parameter w and effective inclination angle v. For orbits in the polar plane (v = 1), it is found that there are two positive solutions to the orbit equation, one is inside and the other is outside the event horizon. Particularly, we obtained the analytical expressions for the radii of these two orbits which are functions of u and w. For orbits in the equatorial plane (v = 0) around an extremal Kerr-Newman black hole (u + w = 1), we find three positive solutions to the equation and provide analytical formulas for the radii of the three orbits. It is also found that a critical value of rotation parameter u = 1 4 exists, above which only one retrograde orbit exists outside the event horizon and below which two orbits (one prograde and one retrograde) exist outside the event horizon. For orbits in the equatorial plane around a nonextremal Kerr-Newman black hole, there are four or two positive solutions to the corresponding sextic equation, which are shown numerically. The number of solutions depends on the choice of parameters in different regions of (u, w)-plane. A critical curve in (u, w)-plane which separates these regions is also obtained. On this critical curve, the explicit formulas of three solutions are found. There always exist two equatorial photon orbits outside the event horizon in the nonextremal Kerr-Newman case. For orbits between the above two special planes, there are four or two solutions to the general sextic equation. When the black hole is extremal, it is found that there is a critical inclination angle vcr, below which only one orbit exists and above which two orbits exist outside the event horizon for a rapidly rotating black hole u > 1 4 . At this critical inclination angle, exact formula for the radii is also derived. Finally, a critical surface in parameter space of (u, w, v) is shown that separates regions with four or two solutions in the nonextremal black hole case.

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Section: Null Geodesics Around Kerr-newman Black Holesmentioning

confidence: 99%

Section: Null Geodesics Around Kerr-newman Black Holesmentioning

confidence: 99%

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Radii of spherical photon orbits around Kerr-Newman black holes

Chen¹,

Huang²,

Jiang³

2022

Preprint

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“…Several numerical examples of spherical photon orbits around a Kerr black hole were plotted by Teo [20,24]. Exact formulas for spherical photon orbits around Kerr black holes were given by Tavlayan and Tekin [25]. The observability of a series of images produced by spherical photon orbits around near-extremal Kerr black holes was shown by Igata et al [26].…”

Section: Introductionmentioning

confidence: 99%

Integrability of Kerr-Newman spacetime with cloud strings, quintessence and electromagnetic field

Cao,

Liu,

2022

Preprint

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The dynamics of charged particles moving around a Kerr-Newman black hole surrounded by cloud strings, quintessence and electromagnetic field is integrable due to the presence of a fourth constant of motion like the Carter constant. The fourth motion constant and the axial-symmetry of the spacetime give a chance to the existence of radial effective potentials with stable circular orbits in two-dimensional planes, such as the equatorial plane and other nonequatorial planes. They also give a possibility of the presence of radial effective potentials with stable spherical orbits in the three-dimensional space. The dynamical parameters play important roles in changing the graphs of the effective potentials. In addition, variations of these parameters affect the presence or absence of stable circular orbits, innermost stable circular orbits, stable spherical orbits and marginally stable spherical orbits. They also affect the radii of the stable circular or spherical orbits. It is numerically shown that the stable circular orbits and innermost stable circular orbits can exist not only in the equatorial plane but also in the nonequatorial planes. Several stable spherical orbits and marginally stable spherical orbits are numerically confirmed, too. In particular, there are some stable spherical orbits and marginally stable spherical orbits with vanishing angular momenta for covering whole the range of the latitudinal coordinate.

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“…One key issue of particular importance is a full understanding of the geodesics -and the fact that despite the lack of spherical symmetry (the Kerr spacetime is merely stationary and axisymmetric, so that the Birkhoff theorem does not apply [22][23][24][25][26]), there are still a multitude of circular geodesics which are not confined to the equatorial plane. (Contrast, for example, [27] with [28][29][30][31][32]. )…”

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confidence: 99%

Constant-$r$ geodesics in the Painleve-Gullstrand form of Lense-Thirring spacetime

Baines¹,

Berry²,

Simpson³

et al. 2022

Preprint

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Herein we explore the non-equatorial circular geodesics (both timelike and null) in the Painlevé-Gullstrand variant of the Lense-Thirring spacetime recently introduced by the current authors. Even though the spacetime is not spherically symmetric, shells of circular geodesics still exist. While the radial motion is (by construction) utterly trivial, determining the allowed locations of these circular geodesics is decidedly nontrivial, and the stability analysis is equally tricky. Regarding the angular motion, these circular orbits will be seen to exhibit both precession and nutation -typically with incommensurate frequencies. Thus circular geodesic motion, though integrable in the technical sense, is generically surface-filling, with the orbits completely covering an equatorial band which is a segment of a sphere, and whose extent is governed by an interplay between the orbital angular momentum and the Carter constant. The situation is qualitatively similar to that for the (exact) Kerr spacetime -but we now see that any physical model having the same slow-rotation weak-field limit as general relativity will still possess non-equatorial circular geodesics.

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Exact formulas for spherical photon orbits around Kerr black holes

Cited by 19 publications

References 18 publications

Radii of spherical photon orbits around Kerr-Newman black holes

Radii of spherical photon orbits around Kerr-Newman black holes

Integrability of Kerr-Newman spacetime with cloud strings, quintessence and electromagnetic field

Constant-$r$ geodesics in the Painleve-Gullstrand form of Lense-Thirring spacetime

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