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. It provides a mathematically elegant extension of previous results to compact objects that carry spin angular momentum and quadrupolar deformations,and solves the isochrone problem of celestial mechanics completely in a geometrical way. It is exceptional in its breadth of scope and achievements,and is clearly and eloquently written,making excellent use of images,providing careful explanations of the concepts and calculations,and conveying the authors personality in a way that is rare in scientific writing.

Format: Hardback
Length: 393 pages
Publication date: 01 May 2023
Publisher: Springer International Publishing AG

The thesis delves into two fascinating and intricate problems in gravitational mechanics, one relativistic and the other Newtonian. The relativistic problem revolves around the first law of binary mechanics, a remarkably straightforward variational relation that holds immense significance in our modern understanding of the gravitational two-body problem. By contributing to the quest to detect gravitational-wave signals from binary systems consisting of black holes and neutron stars, this law plays a pivotal role in advancing our knowledge of the cosmos.

The work presented in the thesis showcases a mathematically elegant extension of previous findings to compact objects that possess spin angular momentum and quadrupolar deformations. These characteristics more accurately represent astrophysical bodies than mere point particles, enhancing our understanding of celestial phenomena.

On the other hand, the Newtonian problem revolves around the isochrone problem of celestial mechanics. Specifically, it involves determining the set of radial potentials that yield bounded orbits with a radial period that remains constant regardless of the angular momentum. The thesis addresses this problem comprehensively through a geometric approach, providing a complete solution. Furthermore, it delves into the consequences of this solution, exploring its impact on various aspects of celestial mechanics, particularly in the characterization of isochrone orbits.

What sets this thesis apart is its remarkable breadth and accomplishments. The writing is clear, concise, and exceptionally well-illustrated, making complex concepts accessible to a wide audience. The authors provide meticulous explanations of the concepts and calculations, ensuring a deep understanding of the subject matter. Additionally, the thesis showcases the author's unique personality, which is rare in scientific writing, without compromising academic rigor.

In summary, the thesis is a groundbreaking work that contributes significantly to gravitational mechanics. Its exploration of relativistic and Newtonian problems, coupled with its mathematical elegance and comprehensive analysis, makes it a valuable contribution to the field. The thesis is exceptional in its scope and achievements, and it is a testament to the author's dedication and expertise.

Weight: 793g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031179631
Edition number: 1st ed. 2023