The First Law of Mechanics in General Relativity & Isochrone Orbits in Newtonian Gravity

The thesis tackles two distinct problems of great interest in gravitational mechanics one relativistic and one Newtonian. The relativistic one is concerned with the "first law of binary mechanics", a remarkably simple variational relation that plays a crucial role in the modern understanding of the gravitational two-body problem, thereby contributing to the effort to detect gravitational-wave signals from binary systems of black holes and neutron stars. The work reported in the thesis provides a mathematically elegant extension of previous results to compact objects that carry spin angular momentum and quadrupolar deformations, which more accurately represent astrophysical bodies than mere point particles.

The Newtonian problem is concerned with the isochrone problem of celestial mechanics, namely the determination of the set of radial potentials whose bounded orbits have a radial period independent of the angular momentum. The thesis solves this problem completely ina geometrical way and explores its consequence on a variety of levels, in particular with a complete characterisation of isochrone orbits.

The thesis is exceptional in the breadth of its scope and achievements. It is clearly and eloquently written, makes excellent use of images, provides careful explanations of the concepts and calculations, and it conveys the author's personality in a way that is rare in scientific writing, while never sacrificing academic rigor.

Nominated as an outstanding PhD thesis by the Université PSL and Observatiore de Paris Includes a review of Isochrony in physics and a complete solution of Henon's isochrone problem Provides new extensions of the First Law of Mechanics for compact objects

Autorentext

Paul Ramond has a Masters degree in Biophysics and one in Theoretical Physics. He completed his PhD in 2022 at the Paris Observatory and Paris University. He now is a postdoc researcher in Paris Dauphine PSL University, with an expertise in the field of gravitational physics, notably the relativistic two-body problem and gravitational Hamiltonian mechanics. He is also engaged in a number of popularization projects (conferences, associations), and enjoys talking about his work to the general public and young students, in particular regarding the applications of science in medicine, biology and music.

Inhalt

Gravitational Theory.- Multipolar Particles.- Helical Isometry.- First Laws of Mechanics.- The First Law at Dipolar Order.