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.
Similar content being viewed by others
References
Abramowicz, M.A. and Kluźniak, W.: 2000, unpublished research notes.
Abramowicz, M.A., Almergren, G.J.E., Kluźniak, W. and Thampan, A.V.: 2003, gr-qc/0312070.
Amsterdamski, P., Bulik, T., Gondek-Rosińska, D. and Kluźniak, W.: 2002, A&A 381, L21.
Kluźniak, W., Abramowicz, M.A., Kato, S., Lee, W.H. and Stergioulas, N.: 2004, ApJ 603, L89.
Kluźniak, W., Bulik, T. and Gondek-Rosińska, D.: 2001, in: B. Battrick (ed.), Exploring the Gamma-Ray Universe. Proceedings of the Fourth INTEGRAL Workshop, Alicante, Spain, 4–8 September 2000, A. Gimenez, V. Reglero and C. Winkler (scientific eds.), ESA SP-459, Noordwijk: ESA Publications Division, pp. 301–304.
Marković, D.: 2000, astro-ph/0009450.
Nowak, M., Lehr, D.: 1999, in: M.A. Abramowicz, G. Björnsson and J.E. Pringle (eds.), Theory of Black Hole Accretion Disks, Cambridge: Cambridge University Press.
Okazaki, A.T., Kato, S. and Fukue, J.: 1987, Publ. Astron. Soc. Jpn. 39, 457.
Perez, C.A., Silbergleit, A.S., Wagoner, R.V. and Lehr, D.E.: 1997, ApJ 476, 589.
Wald, R.W.: 1984, General Relativity, Chicago: University of Chicago Press.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10509-005-1173-z