Gyroscope precession along general timelike geodesics in a Kerr black hole spacetime

Bini, Donato; Geralico, Andrea; Jantzen, Robert T.

doi:10.1103/physrevd.95.124022

Cited by 13 publications

(23 citation statements)

References 58 publications

(88 reference statements)

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“…The orthogonal decomposition into radial and angular directions in the Carter frame is the starting point for solving the equations of parallel transport along a geodesic, as done by Marck and explained geometrically for the simpler case of equatorial plane geodesics in our previous articles [24][25][26].…”

Section: Geodesic Observersmentioning

confidence: 99%

Black hole geodesic parallel transport and the Marck reduction procedure

2019

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The Wigner rotations arising from the combination of boosts along two different directions are rederived from a relative boost point of view and applied to gyroscope spin precession along timelike geodesics in a Kerr spacetime, clarifying the geometrical properties of Marck's recipe for describing parallel transport along such world lines expressed in terms of the constants of the motion. His final angular velocity isolates the cumulative spin precession angular velocity independent of the spacetime tilting required to keep the spin 4-vector orthogonal to the gyro 4-velocity. As an explicit example the cumulative precession effects are computed for a test gyroscope moving along both bound and unbound equatorial plane geodesic orbits.

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Section: Geodesic Observersmentioning

confidence: 99%

Black hole geodesic parallel transport and the Marck reduction procedure

2019

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“…Using the Landau-Lifshitz (1 + 3) -decomposition [8] we observed that, unlike a geodesic equation, the MPTD equations lead to the expression for three-acceleration which contains divergent terms as v → c [9]. Fast test particles are now under intensive investigation [10][11][12][13][14], and represent an important tool in the study, for example, of near horizon geometry of black holes [15][16][17][18][19][20][21][22][23]. So, it would be interesting to find a generalization of MPTD equations with improved behavior in ultra relativistic regime.…”

Section: Introductionmentioning

confidence: 99%

Relativistic effects due to gravimagnetic moment of a rotating body

Ramírez

Дериглазов

2017

Phys. Rev. D

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We compute exact Hamiltonian (and corresponding Dirac brackets) for spinning particle with gravimagnetic moment κ in an arbitrary gravitational background. κ = 0 corresponds to the Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations. κ = 1 leads to modified MPTD equations with reasonable behavior in the ultrarelativistic limit. So we study the modified equations in the leading post-Newtonian approximation. Rotating body with unit gravimagnetic moment has qualitatively different behavior as compared with MPTD body: A) If a number of gyroscopes with various rotation axes are freely traveling together, the angles between the axes change with time. B) For specific binary systems, gravimagnetic moment gives a contribution to frame-dragging effect with the magnitude, that turns out to be comparable with that of Schiff frame dragging.

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“…In the example of Kerr black holes, there are three orthonormal tetrad families, namely, frame of ZAMOs, Carter's frame and static frame [32]. In static frame, the 0-component of tetrad e 0 is along the direction of coordinate time ∂ t .…”

Section: Holesmentioning

confidence: 99%

“…Carter's frame is fundamentally important to properties of geodesic equations and curvature tensors [32]. Grenzebach et al [15] firstly used this orthonormal frame to calculate shadow of Kerr-like black holes.…”

Section: Holesmentioning

confidence: 99%

“…Recently, this approach has been extended by Stuchlik et al [16] to calculate shadow of Kerr-de Sitter black holes. Alternatively, Grenzebach et al [15] firstly used Carter's frame [32] to calculate shadow of Kerr-de Sitter black holes for observers located at finite distance. This approach has also been used in other space-time geometries [22,33].…”

Section: Introductionmentioning

confidence: 99%

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A revisit of rotating black hole shadow with astrometric observables

Chang,

Zhu

2020

Preprint

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The first image of black hole in M87 galaxy taken by Event Horizon Telescope shows that directed observation of supermassive black holes would be a promising way to test general relativity in strong gravity field regime. In order to calculate shadow of rotating black holes with respect to observers located at finite distance, orthonormal tetrads have been introduced in previous works.However, it is noticed that different choice of tetrads does not lead to the same shape of shadow for observers in near regions. In this paper, we alternatively use formula of astrometric observables for calculating the shadow of a general rotating black hole with respect to these observers. For the sake of intuitive, we also consider Kerr-de Sitter black holes as a representative example. In this space-time, size and shape of Kerr-de Sitter black hole shadows are expressed as functions of distance between the black hole and observer. It is forecasted that the distortion of shadow would increase with distance.

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Gyroscope precession along general timelike geodesics in a Kerr black hole spacetime

Cited by 13 publications

References 58 publications

Black hole geodesic parallel transport and the Marck reduction procedure

Black hole geodesic parallel transport and the Marck reduction procedure

Relativistic effects due to gravimagnetic moment of a rotating body

A revisit of rotating black hole shadow with astrometric observables

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