Nonradial stability of marginal stable circular orbits in stationary axisymmetric spacetimes

Ono, Toshiaki; Suzuki, Tomohito; Asada, Hideki

doi:10.1103/physrevd.94.064042

Cited by 6 publications

(5 citation statements)

References 32 publications

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“…The zenithal stability issue in particular axisymmetric spacetimes has been studied recently in Ref. [30] and an analysis using Lyapunov exponent method for general metrics might reveal more general stability conditions on metric functions.…”

Section: Discussionmentioning

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%

“…In the spacetimes possessing axisymmetry, it is often desirable to know the existence and stability of circular orbits (COs) in the equatorial plane. These orbits for example can be used to characterize the properties of the central object [15] or in approximate treatment of more complicated equatorial motion [16] and numerical modeling of stellar systems [17]. They are also of huge importance to the study of flow of matter in the accretion disk around rotating black holes (BHs) or binary systems [18][19][20].…”

Section: Introductionmentioning

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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Section: Discussionmentioning

confidence: 99%

Section: Stability Of Cos and Existence Of Marginally Stable Cosmentioning

confidence: 99%

Section: Introductionmentioning

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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“…Since this family has singularities on the horizon but not outside it, we can examine the existence of the timelike/null geodesic Killing orbits and their stability throughout the domain of outer communication. The geodesic structure of the 4D MP dihole spacetime has been analyzed in detail in terms of circular/bound orbits and their stability [31][32][33][34][35][36][37][38], chaos [39,40], and shadows [41,42]. The particle dynamics in higher-dimensional MP spacetimes were investigated in Ref.…”

Section: Introductionmentioning

confidence: 99%

Stable circular orbits in higher-dimensional multi–black-hole spacetimes

Igata¹,

Tomizawa

2020

Phys. Rev. D

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We consider the dynamics of particles, particularly focusing on circular orbits in the higher-dimensional Majumdar-Papapetrou (MP) spacetimes with two equal mass black holes. It is widely known that in the 5D Schwarzschild-Tangherlini and Myers-Perry backgrounds, there are no stable circular orbits. In contrast, we show that in the 5D MP background, stable circular orbits can always exist when the separation of two black holes is large enough. More precisely, for a large separation, stable circular orbits exist from the vicinity of horizons to infinity; for a medium one, they appear only in a certain finite region bounded by the innermost stable circular orbit and the outermost stable circular orbit outside the horizons; for a small one, they do not appear at all. Moreover, we show that in MP spacetimes in more than 5D, they do not exist for any separations.

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“…To achieve this, we adopt the Majumdar-Papapetrou (MP) dihole spacetime, which contains two extremal Reissner-Nordström black holes. The circular orbit and its stabilities in the equal mass MP dihole spacetime have been investigated [25][26][27]. In our previous paper [25], we clarified the dependence of the positions of MSCOs and ISCOs on the separation parameter in the equal mass MP * Electronic address: nakashi@rikkyo.ac.jp † Electronic address: igata@rikkyo.ac.jp…”

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confidence: 99%

Effect of a second compact object on stable circular orbits

Nakashi

Igata

2019

Phys. Rev. D

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We investigate how stable circular orbits around a main compact object appear depending on the presence of a second one by using the Majumudar-Papapetrou dihole spacetime, which consists of the two extremal Reissner-Nordström black holes with different masses. While the parameter range of the separation of the two objects is divided due to the appearance of stable circular orbits, this division depends on its mass ratio. We show that the mass ratio range separates into four parts, and we find three critical values as the boundaries. I. INTRODUCTIONRecent progress in the observation of gravitational waves supports the existence of binary black hole systems. The LIGO Scientific and Virgo collaborations have already detected gravitational waves ten times from binary black hole mergers and once from a binary neutron star merger so far [1][2][3][4]. Furthermore, since they have started the third observation run, the number of detections will increase in the future. These results imply that binary black hole systems are a quite common phenomenon in our Universe.A pure binary black hole system is a highly idealized model, around which a third object or matter distribution usually exists in realistic situations. Therefore, one of the next issues is clarifying perturbative interactions with a third body around them. As traditional problems in Newtonian gravity, there are Poincaré's three-body problem and the Kozai mechanism. In recent years, some problems related to these topics have been considered in the framework of the relativistic three body problem [5,6], in the context of resonance in a compound extreme mass ratio inspiral/massive black hole binary [7], and in gravitational wave emission induced by a third body [8][9][10][11]. If a third body itself is the target of observation, we can view it as a test body in a fixed background. As a traditional problem in Newtonian gravity, there is Euler's three-body problem, test particle motion in two fixed centers. The corresponding relativistic system is the main topic of this paper.The study of test body motion is significant for the predictions of astrophysical phenomena around a gravitational system such as a binary. In particular, the circular orbit of a test body plays some essential roles in both theory and observations. In the black hole spacetime, for instance, the bending of light due to strong gravity makes a photon orbit circular near the horizon. If the circular photon orbit is unstable, it relates to the formation of the black hole shadow. On the other hand, the sequence of stable circular massive particle orbits is relevant to accretion disks and a binary system. The innermost stable circular orbit (ISCO) radius is a distinctive one because it is identified as the inner edge of a standard accretion disk model and a compact binary switches the stage of the evolution from the inspiraling phase to the merging phase there [12,13].Actual binary black hole systems exist as highly dynamical systems so that one needs to use the numerical method to analyze the phenomen...

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Nonradial stability of marginal stable circular orbits in stationary axisymmetric spacetimes

Cited by 6 publications

References 32 publications

Existence and stability of circular orbits in static and axisymmetric spacetimes

Existence and stability of circular orbits in static and axisymmetric spacetimes

Stable circular orbits in higher-dimensional multi–black-hole spacetimes

Effect of a second compact object on stable circular orbits

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