# Orbits around a Schwarzschild/Kerr black hole

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1. Sep 30, 2014

### FunWarrior

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 Schwarzchild 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 Schwarzchild 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.

2. Oct 1, 2014

### stevebd1

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

3. Oct 1, 2014

### Mentz114

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