Application of Sturm's theorem to marginal stable circular orbits of a test body in spherically symmetric and static spacetimes

Ono, Toshiaki; Suzuki, Tomohito; Fushimi, Naomasa; Yamada, Kazutaka; Asada, Hideki

doi:10.1209/0295-5075/111/30008

Cited by 9 publications

(16 citation statements)

References 36 publications

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“…The wording "marginal stable circular orbits" is used, because the wording "marginally stable" has a different meaning in the theory of dynamical systems. It is interesting to extend such previous works [8,9,11] to stationary and axisymmetric cases, because astrophysical black holes are likely to spin [1,2]. Indeed, Stute and Camenzind have found an equation for the MSCO radius [12], where the particle is assumed to move on the equatorial plane.…”

Section: Introductionmentioning

confidence: 93%

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Nonradial stability of marginal stable circular orbits in stationary axisymmetric spacetimes

Ono¹,

Suzuki²,

Asada³

2016

Phys. Rev. D

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We study linear nonradial perturbations and stability of a marginal stable circular orbit (MSCO) such as the innermost stable circular orbit (ISCO) of a test particle in stationary axisymmetric spacetimes which possess a reflection symmetry with respect to the equatorial plane. A zenithal stability criterion is obtained in terms of the metric components, the specific energy and angular momentum of a test particle. The proposed approach is applied to Kerr solution and MajumdarPapapetrou solution to Einstein equation. Moreover, we reexamine MSCOs for a modified metric of a rapidly spinning black hole that has been recently proposed by Johannsen and Psaltis [PRD, 83, 124015 (2011)]. We show that, for the Johannsen and Psaltis's model, circular orbits that are stable against radial perturbations for some parameter region become unstable against zenithal perturbations. This suggests that the last circular orbit for this model may be larger than the ISCO.

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Section: Introductionmentioning

confidence: 93%

“…Ono et al have recently reexamined, in terms of Sturm's theorem [10], marginal stable circular orbits (MSCOs) of a test particle in spherically symmetric and static spacetimes [11]. The wording "marginal stable circular orbits" is used, because the wording "marginally stable" has a different meaning in the theory of dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

Nonradial stability of marginal stable circular orbits in stationary axisymmetric spacetimes

Ono¹,

Suzuki²,

Asada³

2016

Phys. Rev. D

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“…Observe that (69) reduces immediately to (19) for static, axisymmetric spacetimes as a particular case (ω = 0, equivalently a 1 = b 1 = c 1 = 0).…”

Section: B Homogeneous Orbit Conditionsmentioning

confidence: 99%

“…Motivation for our current work stems from [18] and [19], in which the authors locate MSCOs for generic static, spherically symmetric spacetimes by using the determinant of an associated linear system. By generalizing to the stationary, axisymmetric setting, we find that the metric components and test body parameters still decouple in the MSCO equations, just as in static, spherically symmetric case.…”

Section: Introductionmentioning

confidence: 99%

Marginally stable circular orbits in stationary axisymmetric spacetimes

Beheshti

Gasperin

2016

Phys. Rev. D

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We derive necessary and sufficient conditions for the existence of marginally stable circular orbits (MSCOs) of test particles in a stationary axisymmetric (SAS) spacetime which possesses a reflection symmetry with respect to the equatorial plane; photon orbits and marginally bound orbits (MBOs) are also addressed. Energy and angular momentum are shown to decouple from metric quantities, rendering a purely geometric characterization of circular orbits for this general class of metrics. The subsequent system is analyzed using resultants, providing an algorithmic approach for finding MSCO conditions. MSCOs, photon orbits and MBOs are explicitly calculated for concrete examples of physical interest.

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“…Secondly, COs of some special spacetime might be of great importance for astrophysics and theoretical research of gravity. For example, the inner-most (or marginally) stable COs play an important role in the accretion disk theory [7,6,8] and consequently closely related to the chaotic motion [9] and behavior of gravitational waves originated from the central source such as black hole binaries [10,11]. Study of the COs in black hole spacetimes with electric charge and/or scalar field can also be used to test properties of these black holes such as their no-hair theorem and extremality [13,12,14,15,16] and even the validity of some modified gravity [17,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

Existence and stability of circular orbits in general static and spherically symmetric spacetimes

Jia

Liu

et al. 2018

Gen Relativ Gravit

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Abstract. The existence and stability of circular orbits (CO) in static and spherically symmetric (SSS) spacetime are important because of their practical and potential usefulness. In this paper, using the fixed point method, we first prove a necessary and sufficient condition on the metric function for the existence of timelike COs in SSS spacetimes. After analyzing the asymptotic behavior of the metric, we then show that asymptotic flat SSS spacetime that corresponds to a negative Newtonian potential at large r will always allow the existence of CO. The stability of the CO in a general SSS spacetime is then studied using the Lyapunov exponent method. Two sufficient conditions on the (in)stability of the COs are obtained. For null geodesics, a sufficient condition on the metric function for the (in)stability of null CO is also obtained. We then illustrate one powerful application of these results by showing that an SU(2) Yang-Mills-Einstein SSS spacetime whose metric function is not known, will allow the existence of timelike COs. We also used our results to assert the existence and (in)stabilities of a number of known SSS metrics.

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Application of Sturm's theorem to marginal stable circular orbits of a test body in spherically symmetric and static spacetimes

Cited by 9 publications

References 36 publications

Nonradial stability of marginal stable circular orbits in stationary axisymmetric spacetimes

Nonradial stability of marginal stable circular orbits in stationary axisymmetric spacetimes

Marginally stable circular orbits in stationary axisymmetric spacetimes

Existence and stability of circular orbits in general static and spherically symmetric spacetimes

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