Orbits around a Schwarzschild/Kerr black hole

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SUMMARY

This discussion focuses on the precession of orbits around Schwarzschild and Kerr black holes, specifically the apsidal precession and angular momentum vector precession. For Schwarzschild black holes, an exact expression for the apsidal precession rate exists, derived from elliptical integrals, while the angular momentum vector remains unchanged due to the planar nature of the orbit. The discussion raises questions about the existence of similar expressions for Kerr black holes and seeks freely accessible computational tools for orbit calculations.

PREREQUISITES
  • Understanding of General Relativity concepts
  • Familiarity with Schwarzschild and Kerr black hole metrics
  • Knowledge of elliptical integrals
  • Basic programming skills for using computational tools
NEXT STEPS
  • Research the apsidal precession formula for Schwarzschild black holes
  • Investigate the precession characteristics of Kerr black holes
  • Explore computational tools for simulating black hole orbits, such as Mathematica or Python libraries
  • Read the paper "Geometric transport along circular orbits in stationary axisymmetric spacetimes" for advanced insights
USEFUL FOR

Astronomers, physicists, and students studying black hole dynamics, as well as researchers interested in computational methods for simulating gravitational effects in General Relativity.

FunWarrior
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Hi everybody,

Around a black hole, a test particle can experience two types precession: of its pericenter and of its angular momentum vector. I would like to know if there exist an EXACT expression for the rate at which these two precession occurs both for a Schwarzschild and a Kerr black hole for a given orbit (with known energy and angular momentum vector).

If I am not mistaken, such expressions exist for a Schwarzschild black hole. In this case, there is no precession of the angular momentum vector (the orbit is planar) and the apsidal precession rate is obtained through an elliptical integral. However, I am not sure about the case of a Kerr black hole.

Could you help me with my problem? Also, I was wondering if there exist a freely accessible program to compute such orbits.

Thank you in advance.
 
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You might find the following paper useful-

Geometric transport along circular orbits in stationary axisymmetric spacetimes
Donato Bini, Christian Cherubini, Gianluca Cruciani, Robert T. Jantzen
http://arxiv.org/abs/gr-qc/0407004
 
Here is the exact solution of Schwarzschild elliptical orbits

G. V. Kraniotis, S. B. Whitehouse,
Precession of Mercury in General Relativity, the Cosmological Constant and Jacobi's Inversion
problem.
Preprint http://128.84.158.119/abs/astro-ph/0305181v3
 

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