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Epicyclic Frequencies Derived From The Effective Potential: Simple And Practical Formulae

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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.

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Authors and Affiliations

  1. On Leave from Department of Astrophysics, Göteborg University, Göteborg, Sweden, S-412-96

    M. A. Abramowicz

  2. Department of Theoretical Physics, Chalmers University, Göteborg, Nordita, Copenhagen, Sweden, Denmark, S-412-96

    M. A. Abramowicz

  3. Institute of Astronomy, Zielona Góra University, Zielona Góra, Poland

    W. Kluźniak

  4. Copernicus Centre, Bartycka 18, PL-00-716, Warszawa, Poland

    W. Kluźniak

Authors
  1. M. A. Abramowicz
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  2. W. Kluźniak
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Correspondence to M. A. Abramowicz.

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Abramowicz, M.A., Kluźniak, W. Epicyclic Frequencies Derived From The Effective Potential: Simple And Practical Formulae. Astrophys Space Sci 300, 127–136 (2005). https://doi.org/10.1007/s10509-005-1173-z

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  • DOI: https://doi.org/10.1007/s10509-005-1173-z

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