Constants of motion for constrained Hamiltonian systems: A particle around a charged rotating black hole

Igata, Takahisa; Koike, Tatsuhiko; Ishihara, Hideki

doi:10.1103/physrevd.83.065027

Cited by 20 publications

(18 citation statements)

References 21 publications

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“…In fact, using a method developed by Van Holten [36], Ref. [37] established that there is no conserved quantity associated with the Killing tensor of the Kerr spacetime whenever the external magnetic field is nonzero (see also [38] for a more recent and general analysis). This is further supported by numerical studies of charged particle motion around a magnetized Kerr BH, which evidence chaotic behavior and hence the non-integrability of the equations of motion [39,40].…”

Section: Equations Of Motionmentioning

confidence: 99%

Black hole pulsar

2018

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In anticipation of a LIGO detection of a black hole/neutron star merger, we expand on the intriguing possibility of an electromagnetic counterpart. Black hole/Neutron star mergers could be disappointingly dark since most black holes will be large enough to swallow a neutron star whole, without tidal disruption and without the subsequent fireworks. Encouragingly, we previously found a promising source of luminosity since the black hole and the highly-magnetized neutron star establish an electronic circuit -a black hole battery. In this paper, arguing against common lore, we consider the electric charge of the black hole as an overlooked source of electromagnetic radiation. Relying on the well known Wald mechanism by which a spinning black hole immersed in an external magnetic field acquires a stable net charge, we show that a strongly-magnetized neutron star in such a binary system will give rise to a large enough charge in the black hole to allow for potentially observable effects. Although the maximum charge is stable, we show there is a continuous flux of charges contributing to the luminosity. Most interestingly, the spinning charged black hole then creates its own magnetic dipole to power a black hole pulsar. arXiv:1808.07887v3 [astro-ph.HE]

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Section: Equations Of Motionmentioning

confidence: 99%

Black hole pulsar

2018

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“…Note that, however, the conformal Killing vector is not related to the constant of motion of a massive particle in general. Even if a particle is subject to external forces, it can have a constant of motion as long as the external fields share the spacetime symmetry [11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Scale invariance and constants of motion

Igata

2018

Progress of Theoretical and Experimental Physics

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Scale invariance in the theory of classical mechanics can be induced from the scale invariance of background fields. In this paper we consider the relation between the scale invariance and the constants of particle motion in a self-similar spacetime, only in which the symmetry is well-defined and is generated by a homothetic vector. Relaxing the usual conservation condition by the Hamiltonian constraint in a particle system, we obtain a conservation law holding only on the constraint surface in the phase space. By the conservation law, we characterize constants of motion associated with the scale invariance not only for massless particles but for massive particles and classify the condition for the existence of the constants of motion. Furthermore, we find the explicit form of the constants of motion by solving the conservation equations.

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“…Geodesics of the particles approaching the MOG-BH could be obtained by using Eqs. ( 30) and (34) together we obtain: Here U eff corresponds to a charged particle given by equation ( 36) where positive and negative signs give the path of the outgoing and ingoing particle respectively. Setting E = 1, L z = 2, M = 1, in Eq.…”

Section: Geodesics Of a Charged Particle Moving Around A Mog-bhmentioning

confidence: 99%

“…The metric (3) is invariant under time translation and rotation around symmetry axis. Thus the Killing vectors equations are [34]:…”

Section: Neutral Particle Dynamics Around Mog Black Holementioning

confidence: 99%

Timelike geodesics of a modified gravity black hole immersed in an axially symmetric magnetic field

Hussain

Jamil

2015

Phys. Rev. D

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Abstract:We investigate the dynamics of a neutral and a charged particle around a black hole in modified gravity immersed in magnetic field. Our focus is on the scalar-tensor-vector theory as modified gravity. We are interested to explore the conditions on the energy of the particle under which it can escape to infinity after collision with another neutral particle in the vicinity of the black hole. We calculate escape velocity of particle orbiting in the innermost stable circular orbit (ISCO) after the collision. We study the effects of modified gravity on the dynamics of particles. Further we discuss how the presence of magnetic field in the vicinity of black hole, effects the motion of the orbiting particle. We show that the stability of ISCO increases due to presence of magnetic field. It is observed that a particle can go arbitrary close to the black hole due to presence of magnetic field. Furthermore ISCO for black hole is more stable as compared with Schwarzschild black hole. We also discuss the Lyapunov exponent and the effective force acting on the particle in the presence of magnetic field. * Electronic address: s

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Constants of motion for constrained Hamiltonian systems: A particle around a charged rotating black hole

Cited by 20 publications

References 21 publications

Black hole pulsar

Black hole pulsar

Scale invariance and constants of motion

Timelike geodesics of a modified gravity black hole immersed in an axially symmetric magnetic field

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