Precise relativistic orbits in Kerr and Kerr–(anti) de Sitter spacetimes

Kraniotis, G. V.

doi:10.1088/0264-9381/21/19/016

Cited by 107 publications

(141 citation statements)

References 62 publications

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“…we solve exactly for the first time null spherical polar geodesics in the Kerr-Newman spacetime. The exact solution of the spherical timelike and null geodesics in the Kerr and Kerr-(anti) de Sitter spacetimes-i.e.when the electric charge of the rotating black hole vanishes-have been derived in references [19,25].…”

Section: Spherical Polar Null Geodesics In Kerr-newman Spacetimementioning

confidence: 99%

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Gravitational lensing and frame dragging of light in the Kerr–Newman and the Kerr–Newman (anti) de Sitter black hole spacetimes

Kraniotis

2014

Gen Relativ Gravit

103

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The null geodesics that describe photon orbits in the spacetime of a rotating electrically charged black hole (Kerr-Newman) are solved exactly including the contribution from the cosmological constant. We derive elegant closed form solutions for relativistic observables such as the deflection angle and frame dragging effect that a light ray experiences in the gravitational fields (i) of a Kerr-Newman black hole and (ii) of a Kerr-Newman-de Sitter black hole. We then solve the more involved problem of treating a Kerr-Newman black hole as a gravitational lens, i.e. a KN black hole along with a static source of light and a static observer both located far away but otherwise at arbitrary positions in space. For this model, we derive the analytic solutions of the lens equations in terms of Appell and Lauricella hypergeometric functions and the Weierstraßmodular form. The exact solutions derived for null, spherical polar and non-polar orbits, are applied for the calculation of frame dragging for the orbit of a photon around the galactic centre, assuming that the latter is a Kerr-Newman black hole. We also apply the exact solution for the deflection angle of an equatorial light ray in the gravitational field of a Kerr-Newman black hole for the calculation of bending of light from the gravitational field of the galactic centre for various values of the Kerr parameter, electric charge and impact factor. In addition, we derive expressions for the Maxwell tensor components for a zero-angular-momentum-observer (ZAMO) in the Kerr-Newman-de Sitter spacetime.Keywords Null geodesics · Exact solutions · Kerr-Newman (anti) de Sitter black hole · Gravitational lensing and frame dragging · Weierstraßelliptic functions · Appell-Lauricella hypergeometric functions

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Section: Spherical Polar Null Geodesics In Kerr-newman Spacetimementioning

confidence: 99%

“…The KN(a)dS dynamical system of geodesics is a completely integrable system 1 as was shown in [13,16,18,19] and the geodesic differential equations take the form:…”

Section: Introductionmentioning

confidence: 99%

Gravitational lensing and frame dragging of light in the Kerr–Newman and the Kerr–Newman (anti) de Sitter black hole spacetimes

Kraniotis

2014

Gen Relativ Gravit

103

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“…In this paper we are concerned with the Kerr-de Sitter metric, which describes a rotating black-hole in a space-time with a cosmological constant (Demianski 1973;Carter 1973;Kerr et al 2003;Kraniotis 2004Kraniotis , 2005Kraniotis , 2007. In particular, we want to study the gravito-magnetic (GM) effects in Kerr-de Sitter metric.…”

Section: The Cosmological Constant Is One Of the Candidates To Explaimentioning

confidence: 99%

Gravitomagnetic effects in Kerr-de Sitter space-time

Iorio

Ruggiero

2009

J. Cosmol. Astropart. Phys.

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We explicitly worked out the orbital effects induced on the trajectory of a test particle by the the weak-field approximation of the Kerr-de Sitter metric.It results that the node, the pericentre and the mean anomaly undergo secular precessions proportional to k, which is a measure of the non linearity of the theory.We used such theoretical predictions and the latest observational determinations of the non-standard precessions of the perihelia of the inner planets of the Solar System to put a bound on k getting k ≤ 10 −29 m −2 . The node rate of the LAGEOS Earth's satellite yields k ≤ 10 −26 m −2 . The periastron precession of the double pulsar PSR J0737-3039A/B allows to obtain k ≤ 3 × 10Interpreting k as a cosmological constant Λ, it turns out that such constraints are weaker than those obtained from the Schwarzschild-de Sitter metric.

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“…It should be mentioned here that according to recent observational results [47,48], supermassive black holes including the one in our galactic centre seem to be spinning at considerable rates as described by the Kerr solution, but there is lack of evidence regarding any charged astrophysical black holes. From the theoretical viewpoint, no black hole solution has yet been found which incorporates both the dilaton and de Sitter expansion for the Kerr black hole, though there exit some interesting applications of particle motion in the Kerr-de Sitter metric [49][50][51]. Further, strong gravitational lensing by the Kerr metric itself is endowed with additional features, and the full phenomenological implications are in the process of being worked out [36][37][38].…”

Section: Strong Field Lensing By Dilaton-de Sitter Black Holesmentioning

confidence: 99%

Particle motion and gravitational lensing in the metric of a dilaton black hole in a de Sitter universe

Mukherjee

Majumdar

2007

Gen Relativ Gravit

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We consider the metric exterior to a charged dilaton black hole in a de Sitter universe. We study the motion of a test particle in this metric. Conserved quantities are identified and the Hamilton-Jacobi method is employed for the solutions of the equations of motion. At large distances from the black hole the Hubble expansion of the universe modifies the effective potential such that bound orbits could exist up to an upper limit of the angular momentum per mass for the orbiting test particle. We then study the phenomenon of strong field gravitational lensing by these black holes by extending the standard formalism of strong lensing to the non-asymptotically flat dilaton-de Sitter metric. Expressions for the various lensing quantities are obtained in terms of the metric coefficients.

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Precise relativistic orbits in Kerr and Kerr–(anti) de Sitter spacetimes

Cited by 107 publications

References 62 publications

Gravitational lensing and frame dragging of light in the Kerr–Newman and the Kerr–Newman (anti) de Sitter black hole spacetimes

Gravitational lensing and frame dragging of light in the Kerr–Newman and the Kerr–Newman (anti) de Sitter black hole spacetimes

Gravitomagnetic effects in Kerr-de Sitter space-time

Particle motion and gravitational lensing in the metric of a dilaton black hole in a de Sitter universe

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