03228nam 2200481 450 991072007670332120230801215625.09783031179648(electronic bk.)978303117963110.1007/978-3-031-17964-8(MiAaPQ)EBC7243523(Au-PeEL)EBL7243523(DE-He213)978-3-031-17964-8(OCoLC)1378937198(PPN)269656758(EXLCZ)992655209870004120230801d2023 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierThe First Law of Mechanics in General Relativity and Isochrone Orbits in Newtonian Gravity /Paul RamondFirst edition.Cham, Switzerland :Springer,[2023]©20231 online resource (408 pages)Springer Theses SeriesPrint version: Ramond, Paul The First Law of Mechanics in General Relativity and Isochrone Orbits in Newtonian Gravity Cham : Springer International Publishing AG,c2023 9783031179631 Includes bibliographical references.Gravitational Theory -- Multipolar Particles -- Helical Isometry -- First Laws of Mechanics -- The First Law at Dipolar Order.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 in a 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.Springer theses.General relativity (Physics)General relativity (Physics)530.11Ramond Paul1355781MiAaPQMiAaPQMiAaPQ9910720076703321The First Law of Mechanics in General Relativity and Isochrone Orbits in Newtonian Gravity3418274UNINA