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

Abstract

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.

Invited lecture at the conference "From X-ray Binaries to Quasars: Black Hole Accretion on All Mass Scales", 13-15 July, 2004, Amsterdam

References in corpus (3)

• Relativistic Diskoseismology. I. Analytical Results for 'Gravity Modes'
• Non-linear resonance in the accretion disk of a millisecond pulsar
• Low-mass quark stars as Maclaurin spheroids

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