Spacetime dynamics of spinning particles: Exact electromagnetic analogies

Costa, L. Filipe O.; Natário, José; Zilhão, Miguel

doi:10.1103/physrevd.93.104006

Cited by 38 publications

(76 citation statements)

References 124 publications

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“…We use the signature − + ++; αβγδ ≡ √ −g [αβγδ] denotes the Levi-Civita tensor, and we follow the orientation [1230] = 1 (i.e., in flat spacetime the particle's proper frame are S α = (0, S), µ α = (0, µ). For their precise definition in terms of moments of T αβ and j α , see [6].…”

Section: Notation and Conventionsmentioning

confidence: 99%

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Gravito-electromagnetic analogies

Costa

Natário²

2014

Gen Relativ Gravit

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101

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We reexamine and further develop different gravito-electromagnetic (GEM) analogies found in the literature, and clarify the connection between them. Special emphasis is placed in two exact physical analogies: the analogy based on inertial fields from the so-called "1+3 formalism", and the analogy based on tidal tensors. Both are reformulated, extended and generalized. We write in both formalisms the Maxwell and the full exact Einstein field equations with sources, plus the algebraic Bianchi identities, which are cast as the source-free equations for the gravitational field. New results within each approach are unveiled. The well known analogy between linearized gravity and electromagnetism in Lorentz frames is obtained as a limiting case of the exact ones. The formal analogies between the Maxwell and Weyl tensors are also discussed, and, together with insight from the other approaches, used to physically interpret gravitational radiation. The precise conditions under which a similarity between gravity and electromagnetism occurs are discussed, and we conclude by summarizing the main outcome of each approach.

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Section: Notation and Conventionsmentioning

confidence: 99%

“…(E U ) α ≡ E α ), or the argument of the 3-vector: E(U ) ≡ E, when the meaning is clear. 6. Electromagnetic field.…”

Section: Notation and Conventionsmentioning

confidence: 99%

Gravito-electromagnetic analogies

Costa

Natário²

2014

Gen Relativ Gravit

Self Cite

101

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“…The electric-type tensor is featured in the geodesic deviation equation [34,37,38] have pointed out the role of the magnetic-type tensor in generating a differential precession ΔΩ a for gyroscopes on neighboring geodesics: ΔΩ a ¼ B ab ζ b .…”

Section: Analysis a Tidal Tensorsmentioning

confidence: 99%

Tidal invariants for compact binaries on quasicircular orbits

et al. 2015

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We extend the gravitational self-force approach to encompass "self-interaction" tidal effects for a compact body of mass μ on a quasicircular orbit around a black hole of mass M ≫ μ. Specifically, we define and calculate at OðμÞ (conservative) shifts in the eigenvalues of the electric-and magnetic-type tidal tensors, and a (dissipative) shift in a scalar product between their eigenbases. This approach yields four gauge-invariant functions, from which one may construct other tidal quantities such as the curvature scalars and the speciality index. First, we analyze the general case of a geodesic in a regular perturbed vacuum spacetime admitting a helical Killing vector and a reflection symmetry. Next, we specialize to focus on circular orbits in the equatorial plane of Kerr spacetime at OðμÞ. We present accurate numerical results for the Schwarzschild case for orbital radii up to the light ring, calculated via independent implementations in Lorenz and Regge-Wheeler gauges. We show that our results are consistent with leading-order postNewtonian expansions, and demonstrate the existence of additional structure in the strong-field regime. We anticipate that our strong-field results will inform (e.g.) effective one-body models for the gravitational two-body problem that are invaluable in the ongoing search for gravitational waves.

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“…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]):…”

mentioning

confidence: 99%

“…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]):…”

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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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Spacetime dynamics of spinning particles: Exact electromagnetic analogies

Cited by 38 publications

References 124 publications

Gravito-electromagnetic analogies

Gravito-electromagnetic analogies

Tidal invariants for compact binaries on quasicircular orbits

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

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