5 papers
Quadrupolar tidal effects destroy the integrability of black hole geodesics: analytic proof and numerical evidence of chaos
Paul Ramond
In general relativity, the motion of a test mass around a rotating black hole is described by Kerr geodesics. Owing to the symmetries of the Kerr spacetime, these geodesics possess…
Octupole moments and the non-universality of free-fall in general relativity
Abraham I. Harte, Paul Ramond
Extended bodies in general relativity do not necessarily fall along geodesics, but can be accelerated. These accelerations depend on an object's angular momentum, as well as on its…
Symplectic mechanics of relativistic spinning compact bodies. III. quadratic-in-spin integrability in Type-D Einstein spacetimes: persistence and breakdown
Paul Ramond, Soichiro Isoyama, Adrien Druart
We investigate the integrability of spinning compact body dynamics at quadratic order in spin in four-dimensional Einstein spacetimes admitting a non-degenerate Killing--Yano tenso…
New Methods of Isochrone Mechanics
Paul Ramond, Jérôme Perez
Isochrone potentials, as defined by Michel Hénon in the fifties, are spherically symmetric potentials within which a particle orbits with a radial period that is independent of its…
The Geometry of Isochrone Orbits: from Archimedes' parabolae to Kepler's third law
Paul Ramond, Jérôme Perez
In classical mechanics, the Kepler potential and the Harmonic potential share the following remarkable property: in either of these potentials, a bound test particle orbits with a…