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

Igata, Takahisa; Tomizawa, Shinya

doi:10.1103/physrevd.102.084003

Cited by 8 publications

(4 citation statements)

References 70 publications

(110 reference statements)

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“…We compare our results with the sequences of stable circular orbits in the 5D Majumdar-Papapetrou dihole spacetime with equal mass M * and separation a * [29]. In the vicinity of each pair of sources, we can see the difference between Newtonian gravity, where there exist sequences of stable circular orbits up to an arbitrary neighborhood of the point masses, and general relativity, where a pair of the innermost stable circular orbits appear due to the relativistic effects.…”

Section: Summary and Discussionmentioning

confidence: 88%

“…To approach this problem, we focus on stable circular massive particle orbits in the 5D Majumdar-Papapetrou dihole spacetime, which are caused by the many-body effect of the sources [29,30]. Although it should be noted that relativistic corrections in higher dimensions can affect particle dynamics at infinity, 3 this fact suggests that stable circular orbits also exist in Newtonian gravity.…”

Section: Introductionmentioning

confidence: 99%

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Chaos in a generalized Euler’s three-body problem

Igata¹

2021

Class. Quantum Grav.

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Euler’s three-body problem is the problem of solving for the motion of a particle moving in a Newtonian potential generated by two point sources fixed in space. This system is integrable in the Liouville sense. We consider the Euler problem with the inverse-square potential, which can be seen as a natural generalization of the three-body problem to higher-dimensional Newtonian theory. We identify a family of stable stationary orbits in the generalized Euler problem. These orbits guarantee the existence of stable bound orbits. Applying the Poincaré map method to these orbits, we show that stable bound chaotic orbits appear. As a result, we conclude that the generalized Euler problem is nonintegrable.

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Section: Summary and Discussionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Chaos in a generalized Euler’s three-body problem

Igata¹

2021

Class. Quantum Grav.

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“…Interestingly, one can see from ( 14) that the ISCO exists only in the case of 4-dimensional spacetime. In higher dimensional Schwarzschild-Tangherlini spacetime, there is no ISCO, which indicates absence of stable circular orbits as in the case of the higher dimensional Majumdar-Papapetrou spacetime [24]. It may be treated as strong evidence that the higher dimensions do not play a role in our Universe, which consists of bounded systems.…”

Section: Basic Equationsmentioning

confidence: 93%

Gravitational Capture Cross-Section of Particles by Schwarzschild-Tangherlini Black Holes

2021

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We study the capture cross-section of massless (photon) and massive test particles by the Schwarzschild–Tangherlini black hole, which is a solution of pure general relativity in higher dimensional spacetime with R×SD−2 topology. It is shown that an extra dimension weakens the gravitational attraction of a black hole, and consequently, radii of all the characteristic circular orbits, such as the radius of a photonsphere decrease in the higher dimensions. Furthermore, it is shown that in higher dimensions, there are no stable and bounded circular orbits. The critical impact parameters and capture cross-sections of photons and massive particles are calculated for several higher dimensions and it is shown that they also decrease with increasing dimension. Moreover, we calculate the capture cross-section of relativistic and non-relativistic test particles in the higher dimensions.

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“…Physically, equation ( 16) can be interpreted as a phenomenon related to the motion of a massive-charged particle in a circular orbit [51,52] with a constant radius. Meanwhile, equation (15) represents phenomena related to the motion of a massive-charged particle in a noncircular orbit.…”

Section: Relativistic Precession Orbitmentioning

confidence: 99%

Dynamics of small precession orbit of a massive-charged particle in five-dimensional Reissner-Nordström spacetime model

Alamsyah,

Fitriani,

Aninda

et al. 2024

Phys. Scr.

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This report discusses the dynamics of the small precession orbit of a massive-charged particle by using the Reissner-Nordström metric with an additional spatial dimension. The event horizon of a massive-charged object in the 5 dimension was smaller than that in the 4 dimension. The difference in the size of the massive-charged object event horizon has implications for the spacetime region that can trap massive-charged particles in bound orbits. The space–time region in the 5 dimension was narrower than that in the 4 dimension. Based on a specific condition, we found that the small precession orbital formalism of massive-charged particles in the 5 dimension implies smaller orbital precession fluctuations than those in the 4 dimension. We applied a dynamical system approach to analyze the dynamics of related small precession motions.

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

Cited by 8 publications

References 70 publications

Chaos in a generalized Euler’s three-body problem

Chaos in a generalized Euler’s three-body problem

Gravitational Capture Cross-Section of Particles by Schwarzschild-Tangherlini Black Holes

Dynamics of small precession orbit of a massive-charged particle in five-dimensional Reissner-Nordström spacetime model

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