Investigating spinning test particles: Spin supplementary conditions and the Hamiltonian formalism

Lukes-Gerakopoulos, Georgios; Seyrich, Jonathan; Kunst, Daniela

doi:10.1103/physrevd.90.104019

Cited by 52 publications

(73 citation statements)

References 36 publications

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“…The fundamental point to be emphasized here is that these two conditions, as well as other reasonable conditions in the literature (such as the CorinaldesiPapapetrou condition [54], the"parallel"condition in [39], or the Newton-Wigner condition [55,56], used in Hamiltonian and effective field theory approaches [57][58][59][60][61][62][63]), are, as shown explicitly in [33], equivalent descriptions of the motion of the test particle, the choice between them being a matter of convenience.…”

Section: Equations Of Motion For Spinning Pole-dipole Particlesmentioning

confidence: 99%

“…On the other hand, in some treatments spin conditions for which P α hid = 0 are preferred; that is the case of the Newton-Wigner [55,56] conditionū α ∝ P α /M + u α lab , where u α lab is the 4-velocity of some "laboratory observer" [58] (it may thus be cast as a combination of the Tulczyjew-Dixon and Corinaldesi-Papapetrou conditions). It is of advantage in some Hamiltonian and effective field theory approaches [57][58][59][60][61][62][63] (see also [126,127]) because it leads to canonical Dirac brackets (to linear order in the spin, in the case of curved spacetime [57,61]). The bottom line is that the spin condition is gauge freedom, and as such one should choose, in each application, the one that suits it the most.…”

Section: Conserved Quantities Proper Mass and Work Done By The Fieldsmentioning

confidence: 99%

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Spacetime dynamics of spinning particles: Exact electromagnetic analogies

2016

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We compare the rigorous equations describing the motion of spinning test particles in gravitational and electromagnetic fields, and show that if the Mathisson-Pirani spin condition holds then exact gravito-electromagnetic analogies emerge. These analogies provide a familiar formalism to treat gravitational problems, as well as a means for comparing the two interactions. Fundamental differences are manifest in the symmetries and time projections of the electromagnetic and gravitational tidal tensors. The physical consequences of the symmetries of the tidal tensors are explored comparing the following analogous setups: magnetic dipoles in the field of non-spinning/spinning charges, and gyroscopes in the Schwarzschild, Kerr, and Kerr-de Sitter spacetimes. The implications of the time projections of the tidal tensors are illustrated by the work done on the particle in various frames; in particular, a reciprocity is found to exist: in a frame comoving with the particle, the electromagnetic (but not the gravitational) field does work on it, causing a variation of its proper mass; conversely, for "static observers", a stationary gravitomagnetic (but not a magnetic) field does work on the particle, and the associated potential energy is seen to embody the Hawking-Wald spin-spin interaction energy. The issue of hidden momentum, and its counterintuitive dynamical implications, is also analyzed. Finally, a number of issues regarding the electromagnetic interaction and the physical meaning of Dixon's equations are clarified.

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Section: Equations Of Motion For Spinning Pole-dipole Particlesmentioning

confidence: 99%

Section: Conserved Quantities Proper Mass and Work Done By The Fieldsmentioning

confidence: 99%

Spacetime dynamics of spinning particles: Exact electromagnetic analogies

2016

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“…The motion of spinning test particle in non-homogeneous gravitational fields has been considered in several articles (see [8][9][10][11] and references therein). Most of these studies are restricted to the "pole-dipole" approximation where just monopole (mass) and dipole (rotational angular momentum, i.e., spin) are taken into account [12].…”

Section: Introductionmentioning

confidence: 99%

“…In the literature, several SSCs have been proposed, such as, Tulczyjew [18], Pirani [19], etc. -for details, see [11]. Similarly, the characteristic orbits of spinning particles in non-rotating and rotating axially symmetric space-times, are shifted inward or outward depending on signature of the spin of the particle, with respect to the non-spinning case [20][21][22][23][24][25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Spinning test particles in the γ spacetime

Toshmatov

Malafarina

2019

Phys. Rev. D

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We consider the motion of spinning particles in the field of a well known vacuum static axially-symmetric space-time, known as γ-metric, that can be interpreted as a generalization of the Schwarzschild manifold to include prolate or oblate deformations. We derive the equations of motion for spinning test particles by using the Mathisson-Papapetrou-Dixon equations together with the Tulczyjew spin-supplementary condition, and restricting the motion to the equatorial plane. We determine the limit imposed by super-luminal velocity for the spin of the particle located at the innermost stable circular orbits (ISCO). We show that the particles on ISCO of the prolate γ space-time are allowed to have higher spin than the corresponding ones in the the oblate case. We determine the value of the ISCO radius depending on the signature of the spin-angular momentum, s − L relation, and show that the value of the ISCO with respect to the non spinning case is bigger for sL < 0 and smaller for sL > 0. The results may be relevant for determining the properties of accretion disks and constraining the allowed values of quadrupole moments of astrophysical black hole candidates.

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“…They are widely used now in computations of spin effects in compact binaries and rotating black holes [9][10][11][12][13][14][15][16], so our results may be relevant in this framework. In the multipole approach, x µ (τ ) is called the representative point (centroid) of the body, the antisymmetric spin-tensor S µν (τ ) is associated with the inner angular momentum and the vector P µ (τ ) is called momentum.…”

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confidence: 99%

Mathisson–Papapetrou–Tulczyjew–Dixon equations in ultra-relativistic regime and gravimagnetic moment

Дериглазов

Ramírez

2016

Int. J. Mod. Phys. D

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Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations in the Lagrangian formulation correspond to the minimal interaction of spin with gravity. Due to the interaction, in the Lagrangian equations instead of the original metric g emerges spin-dependent effective metric G = g + h(S). So we need to decide, which of them the MPTD particle sees as the space-time metric. We show that MPTD equations, if considered with respect to original metric, have unsatisfactory behavior: the acceleration in the direction of velocity grows up to infinity in the ultra-relativistic limit. If considered with respect to G, the theory has no this problem. But the metric now depends on spin, so there is no unique space-time manifold for the Universe of spinning particles: each particle probes his own three-dimensional geometry. This can be improved by adding a non-minimal interaction of spin with gravity through gravimagnetic moment. The modified MPTD equations with unit gravimagnetic moment have reasonable behavior within the original metric.Equations of motion of a rotating body in a curved background are formulated usually in the multipole approach to describe the body [1][2][3][4][5][6][7][8]. We consider the Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations, which describe the body in the pole-dipole approximation, in the form studied by Dixon (for the relation of the Dixon equations with those of Papapetrou and Tulczyjew see p. 335 in [4] as well as the recent works [7,8]):(our S µν is twice that of Dixon). They are widely used now in computations of spin effects in compact binaries and rotating black holes [9][10][11][12][13][14][15][16], so our results may be relevant in this framework. In the multipole approach, x µ (τ ) is called the representative point (centroid) of the body, the antisymmetric spin-tensor S µν (τ ) is associated with the inner angular momentum and the vector P µ (τ ) is called momentum.A few words about our notation. As we will discuss the ultra-relativistic limit, we do not assume the proper-time parametrization, that means that we do not add the equation g µνẋ µẋν = −c 2 to the system (1). Our variables are taken in an arbitrary parametrization τ , andẋ µ = , and so on. The notation for the scalar functions constructed from second-rank tensors are θS = θ µν S µν , S 2 = S µν S µν . In the present work we continue the analysis of the MPTD equations on the base of Lagrangian formulation developed in the recent work [17], and discuss the necessity of generalizing the formalism by including an interaction of the spin with gravity through non vanishing gravimagnetic moment. We discuss the behavior of the MPTD-particle in ultra-relativistic limit, when the speed of the particle approximates the speed of light. Since we are interested in the influence of the spin on the particle's trajectory, we eliminate the momenta from the MPTD equations, thus obtaining a second-order equation for the representative point x µ (τ ). To achieve this, we compute the derivative of the spin supplementary condition (SSC), ∇(S µν ...

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Investigating spinning test particles: Spin supplementary conditions and the Hamiltonian formalism

Cited by 52 publications

References 36 publications

Spacetime dynamics of spinning particles: Exact electromagnetic analogies

Spacetime dynamics of spinning particles: Exact electromagnetic analogies

Spinning test particles in the γ spacetime

Mathisson–Papapetrou–Tulczyjew–Dixon equations in ultra-relativistic regime and gravimagnetic moment

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