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Epicyclic frequencies derived from the effective potential: simple and practical formulae

Journal article
Authors Marek A Abramowicz
W. Kluzniak
Published in Astrophys. Space Sci.
Volume 300
Issue 1-3
Pages 127-136
ISSN 0004-640X
Publication year 2005
Published at Department of Physics (GU)
Pages 127-136
Language en
Subject categories Physical Sciences, Astronomy, Astrophysics and Cosmology


We present and discuss a short and simple derivation of orbital epicyclic frequencies for circular geodesic orbits in stationary and axially symmetric spacetimes. Such spacetimes include as special cases analytically known black hole Kerr and Schwarzschild spacetimes, as well as the analytic Hartle-Thorne spacetime and all numerically constructed spacetimes relevant for rotating neutron stars. Our derivation follows directly from energy and angular momentum conservation and it uses the concept of the effective potential. It has never been published, except for a few special cases, but it has already become a part of the common knowledge in the field.

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