Epicyclic Orbital Oscillations in Newton's and Einstein's Dynamics |
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Authors: | Marek A Abramowicz Wlodek Kluźniak |
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Institution: | (1) Institut d'Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France;(2) Department of Astrophysics, Chalmers University, 412-96 Göteborg, Sweden;(3) Institute of Astronomy, Zielona Góra University, Lubuska 2, 65-365 Zielona Góra, Poland |
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Abstract: | We apply Feynman's principle, The same equations have the same solutions, to Kepler's problem and show that Newton's dynamics in a properly curved 3-D space is identical with that described by Einstein's theory in the 3-D optical geometry of Schwarzschild's spacetime. For this reason, rather unexpectedly, Newton's formulae for Kepler's problem, in the case of nearly circular motion in a static, spherically spherical gravitational potential accurately describe strong field general relativistic effects, in particular vanishing of the radial epicyclic frequency at r = r
ms. |
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Keywords: | Equation of motion Schwarzschild spacetime |
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