Marginally stable circular orbits in stationary axisymmetric spacetimes

Beheshti, Shabnam; Gasperin, Edgar

doi:10.1103/physrevd.94.024015

Cited by 11 publications

(14 citation statements)

References 37 publications

(88 reference statements)

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“…This implies that, at least for the Johannsen and Psaltis's model, the last circular orbit might be larger than the ISCO, because the ISCO (in the usual sense) often refers to the smallest circular orbit that is stable against the radial perturbation. [3,5,11,12,[22][23][24]26] It is left as a future work to study a more general case.…”

Section: Discussionmentioning

confidence: 99%

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: Discussionmentioning

confidence: 99%

Nonradial stability of marginal stable circular orbits in stationary axisymmetric spacetimes

Ono¹,

Suzuki²,

Asada³

2016

Phys. Rev. D

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“…For stationary and axisymmetric spacetimes, the most general form of the metric can be given in local coordinates by the Weyl-Lewis-Papapetrou line element [25]…”

Section: Metric Geodesic Equations and Co Conditionsmentioning

confidence: 99%

“…(25) and (26) is satisfied in this region. If no CO exists at all for all ρ > 0, then in the entire range of ρ, either one of (25) or (26) is satisfied, or these two are satisfied piecewisely. Now we further show that the piecewise satisfaction scenario is impossible and then establish one of the main conclusions in this work.…”

Section: This Equation Will Not Have Any Solution In a Region Of ρ Ifmentioning

confidence: 99%

“…(26) is satisfied in the entire range of ρ, but not because Eq. (25) and (26) are piecewisely satisfied.…”

Section: This Equation Will Not Have Any Solution In a Region Of ρ Ifmentioning

confidence: 99%

“…We then use the Lyapunov exponent method [29] to address the question about what form of A(ρ) will make the CO stable, unstable or have a marginal stability. Here we use the wording "marginal stability" instead of "marginally stable" [25] or "marginal stable" [30] because such orbit, defined as dV (ρ * )/dρ = 0, is not necessarily stable even in the perturbative sense. This definition only means that the stability at this point is critical, i.e., it can change, disappear or split in to many equilibria [31].…”

Section: Stability Of Cos and Existence Of Marginally Stable Cosmentioning

confidence: 99%

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Existence and stability of circular orbits in static and axisymmetric spacetimes

Jia¹,

Pang²,

Yang³

2018

Gen Relativ Gravit

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The existence and stability of timelike and null circular orbits (COs) in the equatorial plane of general static and axisymmetric (SAS) spacetime are investigated in this work. Using the fixed point approach, we first obtained a necessary and sufficient condition for the non-existence of timelike COs. It is then proven that there will always exist timelike COs at large ρ in an asymptotically flat SAS spacetime with a positive ADM mass and moreover, these timelike COs are stable. Some other sufficient conditions on the stability of timelike COs are also solved. We then found the necessary and sufficient condition on the existence of null COs. It is generally shown that the existence of timelike COs in SAS spacetime does not imply the existence of null COs, and vice-versa, regardless whether the spacetime is asymptotically flat or the ADM mass is positive or not. These results are then used to show the existence of timelike COs and their stability in an SAS Einstein-Yang-Mills-Dilaton spacetimes whose metric is not completely known. We also used the theorems to deduce the existence of timelike and null COs in some known SAS spacetimes.

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Internal structures and circular orbits for test particles

Zhang

Jiang

2022

Physics Letters B

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Marginally stable circular orbits in stationary axisymmetric spacetimes

Cited by 11 publications

References 37 publications

Nonradial stability of marginal stable circular orbits in stationary axisymmetric spacetimes

Nonradial stability of marginal stable circular orbits in stationary axisymmetric spacetimes

Existence and stability of circular orbits in static and axisymmetric spacetimes

Internal structures and circular orbits for test particles

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