Spinning test particles in Weyl spacetimes

Bini, Donato; Felice, F. de; Geralico, Andrea; Lunari, Andrea

doi:10.1088/0305-4470/38/5/017

Cited by 5 publications

(5 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Spinning particles were also followed in a general class of Weyl space–times. Bini et al (2005c) studied them on circular orbits (and under three main supplementary conditions) in several Weyl fields superposed of Schwarzschild black hole(s) and Chazy–Curzon particle(s), again discussing the corresponding clock effect. A similar analysis was also devoted to motion in the vacuum C‐metric, along circular orbits around the acceleration axis (Bini et al 2005a).…”

Section: Mathisson–papapetrou Equationsmentioning

confidence: 99%

Spinning test particles in a Kerr field - II

Kyrian

Semerák

2007

Monthly Notices of the Royal Astronomical Society

126

210

View full text Add to dashboard Cite

The motion of small spinning free test bodies is usually treated within the 'pole-dipole' approximation, which -in general relativity -leads to Mathisson-Papapetrou (MP) equations. These have to be supplemented by three side constraints in order to provide a unique solution. Several different 'spin conditions' have been proposed and used in the literature, each leading to different worldlines. In a previous paper, we integrated the MP equations with the p σ S μσ = 0 condition numerically in Kerr space-time and illustrated the effect of the spincurvature interaction by comparing the trajectories obtained for various spin magnitudes. Here we also consider other spin conditions and clarify their interrelations analytically as well as numerically on particular trajectories. The notion of a 'minimal worldtube' is introduced in order to judge the individual supplementary conditions and to expose the limitations of the pole-dipole approximation.The motion of extended bodies is a difficult problem even if they do not radiate and do not contribute to the field (are treated as 'test'). However, when the body is small in comparison with the characteristic length of the background field (e.g. in comparison with the distance from the field source), its structure can be described by multipoles and its evolution then expressed in terms of their change. In general relativity, the multipoles are given by integrals,of the energy-momentum tensor T μν , calculated around a certain 'representative' worldline X α (τ ) chosen within the body's history; g ≡ det(g μν ) is the metric-tensor determinant, δx α ≡ x α − X α is a deviation from the representative worldline, running through the volume of the body, and τ is the proper time along the representative worldline (dτ 2 = −g μν dX μ dX ν ). Evolution equations are then obtained by integration of the covariant conservation laws T μν ;ν = 0. They have the form of a series of multipole contributions that generally fall off with n as (R/r) n , where R is the characteristic size of the body and r is the characteristic length of the background space-time. The latter is given by the Riemann curvature tensor R μ νκλ which complicates the equations heavily with increasing n, so that only several-term approximations of the evolution equations are usually employed. The approximation involving just the first two terms (the 'pole-dipole particle') leads to the Mathisson-Papapetrou (MP) equations (Papapetrou 1951): 1 We use geometrized units in which c = G = 1 and the metric signature (−+++). Greek indices run from 0 to 3 and the summation convention is followed. Comma/semicolon in the index denotes the partial/covariant derivative. 2 Please note two omissions that crept into appendix A of Paper I: in the first two lines of the Riemann-tensor Boyer-Lindquist components, sin 2 θ should have been added at R φ ttφ and R φ trθ ; namely, these components should have had −[(2Mar sin 2 θ )/( − a 2 sin 2 θ )] in front.

show abstract

Section: Mathisson–papapetrou Equationsmentioning

confidence: 99%

Spinning test particles in a Kerr field - II

Kyrian

Semerák

2007

Monthly Notices of the Royal Astronomical Society

126

210

View full text Add to dashboard Cite

show abstract

“…[11][12][13][14][15][16]. The existence of analytic solutions is only allowed in special situations which are in general too restrictive to yield a complete description of the nongeodesic motion induced by the structure of the body; for instance, by constraining the path along Killing trajectories in highly symmetric spacetimes, e.g., circular orbits [17][18][19][20][21][22][23], also in the ultrarelativistic regime [24]. Finally, for bodies with structure up to the octupole momentum an action principle formulation of the dynamics has been studied, with applications limited to gravitational phase shift [25].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of quadrupolar bodies in a Schwarzschild spacetime

Bini

Geralico

2013

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

The dynamics of extended bodies endowed with multipolar structure up to the mass quadrupole moment is investigated in the Schwarzschild background according to the Dixon's model, extending previous works. The whole set of evolution equations is numerically integrated under the simplifying assumptions of constant frame components of the quadrupole tensor and that the motion of the center of mass be confined on the equatorial plane, the spin vector being orthogonal to it. The equations of motion are also solved analytically in the limit of small values of the characteristic length scales associated with the spin and quadrupole with respect to the background curvature characteristic length. The results are qualitatively and quantitatively different from previous analyses involving only spin structures. In particular, the presence of the quadrupole turns out to be responsible for the onset of a non-zero spin angular momentum, even if initially absent.

show abstract

“…Following the ideas presented in the latter reference, solutions describing circular or nearly circular orbits in various black hole space-times have been found. Different aspects of such orbits have been studied in the case of Lense-Thirring space-time in [9], in the case of Schwarzschild space-time in [10,11,12,13,14] (also in [15] for non-circular orbits), in the case of Kerr black hole in [16,17,18,19,20,21,22,23,24], in the case of Reissner-Nordström black hole in [25], and in the case of Weyl space-time in [26]. An alternative framework has been used in [27,28] and [29] to study orbits of spinning particles in Schwarzschild and Kerr-Newman space-times respectively.…”

Section: Introductionmentioning

confidence: 99%

Stability of circular orbits of spinning particles in Schwarzschild-like space–times

Mohseni

2010

Gen Relativ Gravit

View full text Add to dashboard Cite

Circular orbits of spinning test particles and their stability in Schwarzschild-like backgrounds are investigated. For these space-times the equations of motion admit solutions representing circular orbits with particles spins being constant and normal to the plane of orbits. For the de Sitter background the orbits are always stable with particle velocity and momentum being co-linear along them. The world-line deviation equations for particles of the same spin-to-mass ratios are solved and the resulting deviation vectors are used to study the stability of orbits. It is shown that the orbits are stable against radial perturbations. The general criterion for stability against normal perturbations is obtained. Explicit calculations are performed in the case of the Schwarzschild space-time leading to the conclusion that the orbits are stable.

show abstract

Spinning test particles in Weyl spacetimes

Cited by 5 publications

References 31 publications

Spinning test particles in a Kerr field - II

Spinning test particles in a Kerr field - II

Dynamics of quadrupolar bodies in a Schwarzschild spacetime

Stability of circular orbits of spinning particles in Schwarzschild-like space–times

Contact Info

Product

Resources

About