Higher-order geodesic deviations applied to the Kerr metric

@article{Colistete2002HigherorderGD,
  title={Higher-order geodesic deviations applied to the Kerr metric},
  author={Roberto Colistete and C{\'e}dric Leygnac and Richard Kerner},
  journal={Classical and Quantum Gravity},
  year={2002},
  volume={19},
  pages={4573-4589}
}
Starting with an exact and simple geodesic, we generate approximate geodesics by summing up higher-order geodesic deviations within a general relativistic setting, without using Newtonian and post-Newtonian approximations. We apply this method to the problem of closed orbital motion of test particles in the Kerr metric spacetime. With a simple circular orbit in the equatorial plane taken as the initial geodesic, we obtain finite eccentricity orbits in the form of Taylor series with the… 
Higher-order geodesic deviations and orbital precession in a Kerr–Newman space–time
A novel approximation method in studying the perihelion precession and planetary orbits in general relativity is to use geodesic deviation equations of first and high-orders, proposed by Kerner et
Geodesic deviations: modeling extreme mass-ratio systems and their gravitational waves
The method of geodesic deviations has been applied to derive accurate analytic approximations to geodesics in Schwarzschild spacetime. The results are used to construct analytic expressions for the
On integrability of the geodesic deviation equation
The Jacobi equation for geodesic deviation describes finite size effects due to the gravitational tidal forces. In this paper we show how one can integrate the Jacobi equation in any spacetime
Higher-order geodesic deviation for charged particles and resonance induced by gravitational waves
We generalize the higher-order geodesic deviation for the structure-less test particles to the higher-order geodesic deviation equations of the charged particles [R. Kerner, J. W. van Holten and R.
On the generalized Jacobi equation
The standard text-book Jacobi equation (equation of geodesic deviation) arises by linearizing the geodesic equation around some chosen geodesic, where the linearization is done with respect to the
Epicycles and Poincare resonances in general relativity
The method of geodesic deviations provides analytic approximations to geodesics in arbitrary background space-times. As such the method is a useful tool in many practical situations. In this note we
Geodesic deviation at higher orders via covariant bitensors
We review a simple but instructive application of the formalism of covariant bitensors, to use a deviation vector field along a fiducial geodesic to describe a neighboring worldline, in an exact and
Interpreting spacetimes of any dimension using geodesic deviation
We present a general method which can be used for geometrical and physical interpretation of an arbitrary spacetime in four or any higher number of dimensions. It is based on the systematic analysis
Jacobi fields, conjugate points and cut points on timelike geodesics in special spacetimes
Several physical problems such as the `twin paradox' in curved spacetimes have purely geometrical nature and may be reduced to studying properties of bundles of timelike geodesics. The paper is a
Spin-induced motion in black hole spacetime
Based on the covariant hamiltonian formalism, we study the dynamics of spinning test bodies in the Kerr and Schwarzschild spacetimes. For the first time, we derive the exact solution of circular
...
...

References

SHOWING 1-10 OF 46 REFERENCES
Relativistic epicycles: another approach to geodesic deviations
We solve the geodesic deviation equations for the orbital motions in the Schwarzschild metric which are close to a circular orbit. It turns out that in this particular case the equations reduce to a
Geodesic deviation in the Schwarzschild space‐time
A general solution of the geodesic deviation equations in the Schwarzschild space‐time is presented. It is found in a rigorous form with the aid of a recently formulated method of integration of the
Motions and worldline deviations in Einstein-Maxwell theory
We examine the motion of charged particles in gravitational and electromagnetic background fields. We study in particular the deviation of worldlines, describing the relative acceleration between
Hamilton-Jacobi formalism for geodesics and geodesic deviations
A formalism of integrating the equations of geodesics and of geodesic deviation is examined based upon the Hamilton–Jacobi equation for geodesics. The latter equation has been extended to the case of
Nodal and periastron precession of inclined orbits in the field of a rotating black hole
The inclination of low-eccentricity orbits is shown to significantly affect orbital parameters, in particular, the Keplerian, nodal precession, and periastron rotation frequencies, which are
Gravitational Wave Induced by a Particle Orbiting around a Schwarzschild Black Hole
We have calculated gravitational waves induced by a test particle with eccentric orbits around a Schwarzschild black hole. The energy and angular momentum fluxes of gravitational waves emitted from
Global structure of the Kerr family of gravitational fields
The Kerr family of solutions of the Einstein and Einstein-Maxwell equations is the most general class of solutions known at present which could represent the field of a rotating neutral or
Gravitational radiation from a particle in circular orbit around a black hole. IV. Analytical results for the slowly rotating case.
  • Poisson
  • Physics
    Physical review. D, Particles and fields
  • 1993
TLDR
Calculations to derive corrections to the gravitational waveforms and luminosity due to the slow rotation of the black hole are presented and in agreement with a more general analysis, based on post-Newtonian theory, by Kidder, Will, and Wiseman.
On one new effect of the Einsteinian theory of gravitation
It is shown by using the equation of geodesic deviation that a small test particle, placed in the centre of inertia of a terrestrial spherical satellite, will vibrate if a small initial momentum
Gravitational Waves by a Particle in Circular Orbits around a Schwarzschild black hole -5.5 Post-Newtonian Formula-
Using the post-Newtonian (PN) expansion technique of the gravitational wave perturbation around a Schwarzschild black hole, we calculate analytically the energy flux of gravitational waves induced by
...
...