On the possibility of non-geodesic motion of massless spinning tops

Armaza, Cristóbal; Hojman, Sergio A.; Koch, Benjamin; Zalaquett, Nicolás

doi:10.1088/0264-9381/33/14/145011

Cited by 13 publications

(30 citation statements)

References 43 publications

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“…First, the critical speed, which the particle can not overcome during its evolution in gravitational field, can be more than the speed of light. The same observation has been made from analysis of MPTD particle in specific metrics [49][50][51][52][53]. Second, the longitudinal acceleration grows up to infinity in the ultrarelativistic limit.…”

Section: Advances In Mathematical Physicssupporting

confidence: 60%

Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

Дериглазов

Ramírez

2017

Advances in Mathematical Physics

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We review the recent results on development of vector models of spin and apply them to study the influence of spin-field interaction on the trajectory and precession of a spinning particle in external gravitational and electromagnetic fields. The formalism is developed starting from the Lagrangian variational problem, which implies both equations of motion and constraints which should be presented in a model of spinning particle. We present a detailed analysis of the resulting theory and show that it has reasonable properties on both classical and quantum level. We describe a number of applications and show how the vector model clarifies some issues presented in theoretical description of a relativistic spin: (A) one-particle relativistic quantum mechanics with positive energies and its relation with the Dirac equation and with relativistic Zitterbewegung; (B) spin-induced noncommutativity and the problem of covariant formalism; (C) three-dimensional acceleration consistent with coordinate-independence of the speed of light in general relativity and rainbow geometry seen by spinning particle; (D) paradoxical behavior of the Mathisson-PapapetrouTulczyjew-Dixon equations of a rotating body in ultrarelativistic limit, and equations with improved behavior.

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Section: Advances In Mathematical Physicssupporting

confidence: 60%

Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

Дериглазов

Ramírez

2017

Advances in Mathematical Physics

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“…Thus, the critical speed does not always coincide with the speed of light and, in general case, we expect that v cr is both field and spin-dependent quantity. The same conclusion follows from analytic and numeric computations on some specific backgrounds [22,23].…”

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confidence: 65%

“…The double squareroot structure in the expression (5) seems to be typical for the spin vector models [20][21][22][23]. In the spinless limit, that is α = 0 and ω µ = 0, the expression (5) reduces to the standard Lagrangian of a relativistic particle, −mc −ẋ µẋ µ .…”

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confidence: 99%

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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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“…Note that if causality is not violated over distances larger than the wavelength of the photon, it should not imply any problem, since the pole-dipole approximation as such only holds if the length scales tied to the particle (here wavelength of the photon) are much smaller than the curvature length scale. Indeed, in papers where the Tulczyjew SSC was employed, e.g., to study photons in the Schwarzschild, de Sitter or FLRW backgrounds [23,39,41,42], causality has not been found to be violated over meaningful distances.…”

Section: )mentioning

confidence: 99%

How does the photon’s spin affect gravitational wave measurements?

Marsot

2019

Phys. Rev. D

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We study the effect of the polarization of light beams on the time delay measured in Gravitational Wave experiments. To this end, we consider the Mathisson-Papapetrou-Dixon equations in a gravitational wave background, with two of the possible spin supplementary conditions: by Frenkel-Pirani, or by Tulczyjew. In the first case, photons follow a null geodesic and thus no spin effect is present. The second case shows a deviation of the photons from the null geodesic, resulting in a tiny effect on the measured time delay of photons depending on their polarization state.

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On the possibility of non-geodesic motion of massless spinning tops

Cited by 13 publications

References 43 publications

Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

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

How does the photon’s spin affect gravitational wave measurements?

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