Motion of test particles in the field of a naked singularity

Boshkayev, Kuantay; Gasperin, Edgar; Gutiérrez-Piñeres, Antonio C.; Quevedo, Hernando; Тоktarbay, С.

doi:10.1103/physrevd.93.024024

Cited by 74 publications

(83 citation statements)

References 30 publications

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“…If the photon orbit is radially stable, timelike circular geodesics are allowed only for r < r ph and are radially stable locally. This behavior is seen in many spacetimes with photon orbits and no horizon [10][11][12][13][14]. Our findings demonstrate that the full linear stability analysis near stable photon orbits relies heavily on the properties of off-equatorial motion and, by Eqs.…”

Section: Discussionmentioning

confidence: 64%

Curvature dependence of relativistic epicyclic frequencies in static, axially symmetric spacetimes

2017

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The sum of squared epicyclic frequencies of nearly circular motion (ω 2 r + ω 2 θ ) in axially symmetric configurations of Newtonian gravity is known to depend both on the matter density and on the angular velocity profile of circular orbits. It was recently found that this sum goes to zero at the photon orbits of Schwarzschild and Kerr spacetimes. However, these are the only relativistic configurations for which such result exists in the literature. Here, we extend the above formalism in order to describe the analogous relation for geodesic motion in arbitrary static, axially symmetric, asymptotically flat solutions of general relativity. The sum of squared epicyclic frequencies is found to vanish at photon radii of vacuum solutions. In the presence of matter, we obtain that ω 2 r + ω 2 θ > 0 for perturbed timelike circular geodesics on the equatorial plane if the strong energy condition holds for the matter-energy fluid of spacetime; in vacuum, the allowed region for timelike circular geodesic motion is characterized by the inequality above. The results presented here may be of use to shed light on general issues concerning the stability of circular orbits once they approach photon radii, mainly the ones corresponding to stable photon motion.

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Section: Discussionmentioning

confidence: 64%

Curvature dependence of relativistic epicyclic frequencies in static, axially symmetric spacetimes

2017

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“…From the positivity condition of the Arnowitt-Deser-Misner mass, the condition 1 q   follows [13]. The interval   exists the third singularity [13], determined by the equation …”

Section: Introductionmentioning

confidence: 99%

Motion of spin-half particles in the axially symmetric field of naked singularities of the static q-metric

Neznamov¹,

Shemarulin²

2017

Gravit. Cosmol.

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“…We expect to perform such an analysis in a future work by applying the procedure shown, for instance, in Ref. 24.…”

Section: Resultsmentioning

confidence: 99%

Geodesics in the field of a rotating deformed gravitational source

Boshkayev

Quevedo

Abutalip

et al. 2016

Int. J. Mod. Phys. A

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We investigate equatorial geodesics in the gravitational field of a rotating and deformed source described by the approximate Hartle-Thorne metric. In the case of massive particles, we derive within the same approximation analytic expressions for the orbital angular velocity, the specific angular momentum and energy, and the radii of marginally stable and marginally bound circular orbits. Moreover, we calculate the orbital angular velocity and the radius of lightlike circular geodesics. We study numerically the frame dragging effect and the influence of the quadrupolar deformation of the source on the motion of test particles. We show that the effects originating from the rotation can be balanced by the effects due to the oblateness of the source.

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Motion of test particles in the field of a naked singularity

Cited by 74 publications

References 30 publications

Curvature dependence of relativistic epicyclic frequencies in static, axially symmetric spacetimes

Curvature dependence of relativistic epicyclic frequencies in static, axially symmetric spacetimes

Motion of spin-half particles in the axially symmetric field of naked singularities of the static q-metric

Geodesics in the field of a rotating deformed gravitational source

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