Gravitational waves from the Hénon-Heiles system

Kokubun, Fernando

doi:10.1103/physrevd.57.2610

Cited by 18 publications

(20 citation statements)

References 9 publications

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“…So far, there were two works on the energy emission rate and the amplitude of the gravitational waves for chaotic systems [21], [22]. In [21], the author calculated the energy emission rate from a particle moving in the Henon-Héiles potential.…”

Section: B Energy Emission Ratementioning

confidence: 99%

“…a particle leaving from the equatorial plane, whereas the motion of a particle in [21] and [22] is restricted to single plane .…”

Section: B Energy Emission Ratementioning

confidence: 99%

“…In [21], the author calculated the energy emission rate from a particle moving in the Henon-Héiles potential. In [22], they analyzed the motion of a (spinless) particle in the Majumder-Papapetrou spacetime with two black holes.…”

Section: B Energy Emission Ratementioning

confidence: 99%

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Signature of chaos in gravitational waves from a spinning particle

Suzuki

Maeda

1999

Phys. Rev. D

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A spinning test particle around a Schwarzschild black hole shows a chaotic behavior, if its spin is larger than a critical value. We discuss whether or not some peculiar signature of chaos appears in the gravitational waves emitted from such a system. Calculating the emitted gravitational waves by use of the quadrupole formula, we find that the energy emission rate of gravitational waves for a chaotic orbit is about 10 times larger than that for a circular orbit, but the same enhancement is also obtained by a regular "elliptic" orbit. A chaotic motion is not always enhance the energy emission rate maximally. As for the energy spectra of the gravitational waves, we find some characteristic feature for a chaotic orbit. It may tell us how to find out a chaotic behavior of the system. Such a peculiar behavior, if it will be found, may also provide us some additional informations to determine parameters of a system such as a spin.

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Section: B Energy Emission Ratementioning

confidence: 99%

“…a particle leaving from the equatorial plane, whereas the motion of a particle in [21] and [22] is restricted to single plane .…”

Section: B Energy Emission Ratementioning

confidence: 99%

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Signature of chaos in gravitational waves from a spinning particle

Suzuki

Maeda

1999

Phys. Rev. D

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“…The general solutions of the Hénon-Heiles system are known only in integrable cases [37,38,11], in other cases not only four-, but even three-parameter exact solutions have yet to be found. The generalized Hénon-Heiles system has attracted enormous attention over the years and has used as a model in astronomy [30] and in gravitation [25,32].…”

Section: The Hénon-heiles Systemmentioning

confidence: 99%

Construction of Special Solutions for Nonintegrable Systems

Vernov¹

2006

JNMP

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The Painlevé test is very useful to construct not only the Laurent series solutions of systems of nonlinear ordinary differential equations but also the elliptic and trigonometric ones. The standard methods for constructing the elliptic solutions consist of two independent steps: transformation of a nonlinear polynomial differential equation into a nonlinear algebraic system and a search for solutions of the obtained system. It has been demonstrated by the example of the generalized Hénon-Heiles system that the use of the Laurent series solutions of the initial differential equation assists to solve the obtained algebraic system. This procedure has been automatized and generalized on some type of multivalued solutions. To find solutions of the initial differential equation in the form of the Laurent or Puiseux series we use the Painlevé test. This test can also assist to solve the inverse problem: to find the form of a polynomial potential, which corresponds to the required type of solutions. We consider the five-dimensional gravitational model with a scalar field to demonstrate this.

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“…The generalized Hénon-Heiles system is a model widely used in astronomy [5] and physics, for example, in gravitation [6,7].…”

Section: Introductionmentioning

confidence: 99%

On two nonintegrable cases of the generalized Hénon-Heiles system

Vernov

Timoshkova

2005

Phys. Atom. Nuclei

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The generalized Hénon-Heiles system with an additional nonpolynomial term is considered. In two nonintegrable cases new two-parameter solutions have been obtained in terms of elliptic functions. These solutions generalize the known oneparameter solutions. The singularity analysis shows that it is possible that threeparameter single-valued solutions exist in these two nonintegrable cases. The knowledge of the Laurent series solutions simplifies search of the elliptic solutions and allows to automatize it.

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Gravitational waves from the Hénon-Heiles system

Abstract: In this work we analyze the emission of gravitational waves from the Hénon-Heiles system. We show the qualitative differences among emission of the gravitational waves from regular and chaotic motions.

Cited by 18 publications

References 9 publications

Signature of chaos in gravitational waves from a spinning particle

Signature of chaos in gravitational waves from a spinning particle

Construction of Special Solutions for Nonintegrable Systems

On two nonintegrable cases of the generalized Hénon-Heiles system

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