Gyroscope precession along bound equatorial plane orbits around a Kerr black hole

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

doi:10.1103/physrevd.94.064066

Cited by 17 publications

(36 citation statements)

References 39 publications

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“…The orbit thus oscillates between a minimum radius r peri (χ = 0, periastron) and a maximum radius r apo (χ = π, apastron). The background motion is governed by the following equations [23,24]…”

Section: Perturbations On a Kerr Spacetimementioning

confidence: 99%

New gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole: Redshift invariant

Bini

Geralico

2019

Phys. Rev. D

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The Detweiler-Barack-Sago redshift function for particles moving along slightly eccentric equatorial orbits around a Kerr black hole is currently known up to the second order in eccentricity, second order in spin parameter, and the 8.5 post-Newtonian order. We improve the analytical computation of such a gauge-invariant quantity by including terms up to the fourth order in eccentricity at the same post-Newtonian approximation level. We also check that our results agrees with the corresponding post-Newtonian expectation of the same quantity, calculated by using the currently known Hamiltonian for spinning binaries.

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Section: Perturbations On a Kerr Spacetimementioning

confidence: 99%

New gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole: Redshift invariant

Bini

Geralico

2019

Phys. Rev. D

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“…In this paper, we discuss how one can distinguish a rotating BH from NS using the behavior of the precession frequency of the spin of a test gyro which moves, in general, along a non-geodetic orbit around such a Kerr compact object, thus generalizing the earlier work on distinguishing black holes from naked singularities. In this regard, we find it useful to mention that recently Bini et al have analyzed the precession of a test gyroscope along bound [5] and unbound [6] equatorial plane geodesic orbits around a BH with respect to a static reference frame whose axes point towards 'fixed stars.' It is well known that the paths followed by spinning test particles are not, in general, geodesics [7,8].…”

Section: Introductionmentioning

confidence: 99%

Distinguishing Kerr naked singularities and black holes using the spin precession of a test gyro in strong gravitational fields

et al. 2017

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“…(iv) Gyroscope precession: The calculation of precession of spin of a test gyroscope is another application for the test of general relativity. In previous studies, approximate expressions were used for the fundamental frequencies as a series expansion in terms of eccentricity up to order e 2 around a Kerr black hole for the stable bound orbits in the equatorial plane [18]. Our exact analytic results are useful to estimate more accurate results which are useful to explain the reported results of geodetic drift rate and frame-dragging drift rate by the Gravity Probe B (GP-B) [45].…”

Section: Applicationsmentioning

confidence: 99%

Astrophysically relevant bound trajectories around a Kerr black hole

Rana¹,

Mangalam

2019

Class. Quantum Grav.

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We derive alternate and new closed-form analytic solutions for the non-equatorial eccentric bound trajectories, {φ (r, θ), t (r, θ) , r (θ)}, around a Kerr black hole by using the transformation 1/r = µ (1 + e cos χ). The application of the solutions is straightforward and numerically fast. We obtain and implement translation relations between energy and angular momentum of the particle, (E, L), and eccentricity and inverse-latus rectum, (e, µ), for a given spin, a, and Carter's constant, Q, to write the trajectory completely in the (e, µ, a, Q) parameter space. The bound orbit conditions are obtained and implemented to select the allowed combination of parameters (e, µ, a, Q). We also derive specialized formulae for equatorial, spherical and separatrix orbits. A study of the non-equatorial analog of the previously studied equatorial separatrix orbits is carried out where a homoclinic orbit asymptotes to an energetically bound spherical orbit. Such orbits simultaneously represent an eccentric orbit and an unstable spherical orbit, both of which share the same E and L values. We present exact expressions for e and µ as functions of the radius of the corresponding unstable spherical orbit, r s , a, and Q, and their trajectories, for (Q = 0) separatrix orbits; they are shown to reduce to the equatorial case. These formulae have applications to study the gravitational waveforms from extreme-mass ratio inspirals (EMRIs) using adiabatic progression of a sequence of Kerr geodesics, besides relativistic precession and phase space explorations. We obtain closed-form expressions of the fundamental frequencies of non-equatorial eccentric trajectories that are equivalent to the previously obtained quadrature forms and also numerically match with the equivalent formulae previously derived. We sketch non-equatorial eccentric, separatrix, zoom-whirl, and spherical orbits, and discuss their astrophysical applications.

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Gyroscope precession along bound equatorial plane orbits around a Kerr black hole

Cited by 17 publications

References 39 publications

New gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole: Redshift invariant

New gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole: Redshift invariant

Distinguishing Kerr naked singularities and black holes using the spin precession of a test gyro in strong gravitational fields

Astrophysically relevant bound trajectories around a Kerr black hole

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