11 citations · 51 across the 11 of their papers we have counts for
11 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…
Symplectic mechanics of relativistic spinning compact bodies II.: Canonical formalism in the Schwarzschild spacetime
Paul Ramond, Soichiro Isoyama
This work constitutes the second part of a series of studies that aim to utilise tools from Hamiltonian mechanics to investigate the motion of an extended body in general relativit…
On the integrability of extended test body dynamics around black holes
Paul Ramond
In general relativity, the motion of an extended test body is influenced by its proper rotation, or spin. We present a covariant and physically self-consistent Hamiltonian framewor…
Symplectic mechanics of relativistic spinning compact bodies. I. linear-in-spin integrability under Killing-Yano symmetry
Paul Ramond, Soichiro Isoyama
We study the Hamiltonian dynamics of a neutral, massive spinning test body at linear order in spin, as governed by the Mathisson--Papapetrou--Tulczyjew--Dixon equations in a 4-dime…
First Law of Mechanics for Spinning Compact Binaries: Dipolar Order
Paul Ramond, Alexandre Le Tiec
Building upon the Noether charge formalism of Iyer and Wald, we derive a variational formula for spacetimes admitting a Killing vector field, for a generic energy-momentum distribu…
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…
Abel-Ruffini's Theorem: Complex but Not Complicated!
Paul Ramond
In this article, using only elementary knowledge of complex numbers, we sketch a proof of the celebrated Abel--Ruffini theorem, which states that the general solution to an algebra…
Multipolar Particles in Helically Symmetric Spacetimes
Paul Ramond, Alexandre Le Tiec
We consider a binary system of spinning compact objects with internal structure, moving along an exactly circular orbit, and modelled within the multipolar gravitational skeleton f…
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…