Epicyclic orbital oscillations in Newton's and Einstein's dynamics

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 the marginally stable orbit.

8 pages

Cited by in corpus (26)

• Non-linear resonance in nearly geodesic motion in low-mass X-ray binaries
• Rotating black holes in Einstein-Dilaton-Gauss-Bonnet gravity with finite coupling
• How to tell an accreting boson star from a black hole
• A Model for High Frequency Quasi-periodic Oscillations from Accreting Black Holes
• Measuring mass and angular momentum of black holes with high-frequency quasi-periodic oscillations
• Testing Gravity with Quasi Periodic Oscillations from accreting Black Holes: the Case of Einstein-Dilaton-Gauss-Bonnet Theory
• The upper kHz QPO: a gravitationally lensed vertical oscillation
• On the time variability of geometrically-thin black hole accretion disks I : the search for modes in simulated disks
• Epicyclic oscillations of fluid bodies Paper II. Strong gravity
• Interpreting the High Frequency QPO Power Spectra of Accreting Black Holes
• Constraining Black Holes with Light Boson Hair and Boson Stars using Epicyclic Frequencies and QPOs
• Magnetic inversion as a mechanism for the spectral transition of black hole binaries
• Testing General Relativity's No-Hair Theorem with X-Ray Observations of Black Holes
• Of NBOs and kHz QPOs: a low-frequency modulation in resonant oscillations of relativistic accretion disks
• Testing Chern-Simons gravity with black holes?
• Ultrastatic spacetimes
• Studies of the Origin of High-Frequency Quasi-Periodic Oscillations of Mass Accreting Black Holes in X-ray Binaries with Next-Generation X-ray Telescopes
• Period doubling and non-linear resonance in the black hole candidate IGR J17091-3624 ?
• Generalized Paraxial Ray Trace Procedure Derived from Geodesic Deviation
• The autoparametric 3:2 resonance in conservative systems
• Optical geometry analysis of the electromagnetic self-force
• Epicyclic orbital oscillations in Newton's and Einstein's gravity from the geodesic deviation equation
• Resonance conditions
• Orbital Motion in Spacetimes Influenced by the Presence of Scalar and Electromagnetic Fields
• Interpreting gravitational fields of Topologically Massive Gravity using geodesic deviation
• Using Simulations of Black Holes to Study General Relativity and the Properties of Inner Accretion Flow