Carter constant and angular momentum

Mukherjee, Sajal; Nayak, K. Rajesh

doi:10.1142/s0218271817501802

Cited by 5 publications

(3 citation statements)

References 15 publications

(6 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, it did not receive much attention until Carter came up with this non-trivial constant to describe the geodesic motion in a Kerr black hole. It turns out that this constant is closely related to the total angular momentum of a particle and for a static spacetime it is exactly same as the square of total angular momentum [41][42][43]. Presence of this constant makes the trajectories completely integrable in the Kerr spacetime.…”

Section: Conserved Quantities : Energy Momentum and Carter Constantmentioning

confidence: 99%

Off-equatorial stable circular orbits for spinning particles

Mukherjee

Nayak

2018

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

In this article, we investigate the motion of a spinning particle at a constant inclination, different from the equatorial plane, around a Kerr black hole. We mainly explore the possibilities of stable circular orbits for different spin supplementary conditions. The Mathisson-Papapetrou's equations are extensively applied and solved within the framework of linear spin approximation. We explicitly show that for a given spin vector of the form S a = 0, S r , S θ , 0 , there exists an unique circular orbit at (rc, θc) defined by the simultaneous minima of energy, angular momentum and Carter constant. This corresponds to the Innermost Stable Circular Orbit (ISCO) which is located on a non-equatorial plane. We further establish that the location (rc, θc) of the ISCO for a given spinning particle depends on the radial component of the spin vector (S r ) as well as the angular momentum of the black hole (J). The implications of using different spin supplementary conditions are investigated. * sm13ip029@iiserkol.ac.in † rajesh@iiserkol.ac.in arXiv:1804.06070v2 [gr-qc]

show abstract

Section: Conserved Quantities : Energy Momentum and Carter Constantmentioning

confidence: 99%

Off-equatorial stable circular orbits for spinning particles

Mukherjee

Nayak

2018

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

show abstract

“…Below we discuss the behavior of the Carter constant if we switch on the external magnetic field. In order to investigate that, we employ the Carter's theorem [44] (see also [45], where this theorem is used explicitly). This theorem states that if we can write down the Hamiltonian in a stationary axis-symmetric spacetime (the form of the metric is given in Eq.…”

Section: Conserved Quantitiesmentioning

confidence: 99%

Resonance crossing of a charged body in a magnetized Kerr background: an analogue of extreme mass ratio inspiral

Mukherjee¹,

Kopáček²,

Lukes-Gerakopoulos³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

“…Typically speaking, the starting of any resonance event would indicate an invitation to the non-integrability of Hamiltonian and therefore the system slowly descends into chaos. However, for a sufficient small perturbation, the system may remain integrable and the notion of separability constant (also known as Carter constant in the black hole spacetime) may still exist [40][41][42]. In case of a spinning particle, the motion is completely integrable upto the linear order and therefore we presume that the addition of spin would not introduce any chaos in the system as far as the O(S 2 ) terms are neglected.…”

Section: Introductionmentioning

confidence: 98%

Resonant orbits for a spinning particle in Kerr spacetime

Mukherjee¹,

Tripathy²

2019

Preprint

Self Cite

View full text Add to dashboard Cite

In the present article, we study the orbital resonance corresponds to an extended object approximated up to the dipole order term in Kerr spacetime. We start with the Mathisson-Papapetrou equations under the linear spin approximation and primarily concentrate on two particular events. First, when the orbits are nearly circular and executing a small oscillation about the equatorial plane and second, a generic trajectory confined on the equatorial plane. While in the first case, all the three fundamental frequencies, namely, radial Ωr, angular Ω θ , azimuthal Ω φ can be commensurate with each others and give rise to the resonance phenomenon, the later is only accompanied with the resonance between Ωr and Ω φ as we set θ = π/2. We provide a detail derivation in locating the prograde resonant orbits in either of these cases and also study the role played by the spin of the black hole. The implications related to spin-spin interactions between the object and black hole are also demonstrated.

show abstract

Carter constant and angular momentum

Cited by 5 publications

References 15 publications

Off-equatorial stable circular orbits for spinning particles

Off-equatorial stable circular orbits for spinning particles

Resonance crossing of a charged body in a magnetized Kerr background: an analogue of extreme mass ratio inspiral

Resonant orbits for a spinning particle in Kerr spacetime

Contact Info

Product

Resources

About