A Mathematical Journey to Relativity: UNITEXT for Physics

Euclidean and Non-­Euclidean Geometries: How they appear.- Basic Facts in Euclidean and Minkowski Plane Geometry.- From Projective Geometry to Poincaré Disk. How to carry out a Non-Euclidean Geometry Model.- Revisiting the Differential Geometry of Surfaces in 3D-Spaces.- Basic Differential Geometry Concepts and their Applications.- Differential Geometry at Work: Two Ways of Thinking the Gravity. The Einstein Field Equations from a Geometric Point of View.- Differential Geometry at Work: Euclidean, Non-Euclidean and Elliptic Geometric Models from Geometry and Physics.- Gravity in Newtonian Mechanics.- Special Relativity.- General Relativity and Relativistic Cosmology.- A Geometric Realization of Relativity: the de Sitter Spacetime.- Another Geometric Realization of Relativity: the Anti-de Sitter Spacetime.- More than Metric: Geometric Objects for Alternative Pictures of Gravity.- Metric-Affine Theories of Gravity.- Conclusions

“All proofs presented in the book are given in detail and are characterized by the necessary rigor. Scattered throughout the book are many problems and exercises together with their solutions illuminating the theory. The book, addressing undergraduate students of physics and mathematics as well, is certainly a valuable addition to the existing relevant literature.” (Theophanes Grammenos, Mathematical Reviews, July, 2022)

Wladimir-Georges Boskoff graduated from the Faculty of Mathematics, University of Bucharest in 1982 and completed his Ph.D. at the same university in 1994. Since 1990 he has been a member of the Department of Mathematics at the Ovidius university, teaching courses on various subjects, including Euclidean and non-Euclidean geometry, differential geometry, calculus on manifolds, mechanics and relativity, astronomy, and other subjects. His scientific papers and books relate to the foundations of geometry, Euclidean and hyperbolic geometry, metric geometry, differential geometry, modified theories of gravity, general relativity, and the history of mathematics. He has been an invited speaker at conferences in France, Japan, the USA, Greece, Italy, and Chile. He is a recipient of the Academy of Sciences of Romania's G. Tzitzeica Prize for contributions to geometry (1996), and the Romanian Mathematical Society Medal for contributions at mathematical education (2010).
 Salvatore Capozziello is  Full Professor of Astronomy and Astrophysics at the Department of Physics at the Università di Napoli "Federico II" where he teaches General Relativity and Cosmology. He is visiting Professor at the Gran Sasso Science Institute (L'Aquila, Italy),  Honorary Professor at the Tomsk State Pedagogical University (Tomsk, Russia), Member of the Lepage Research Institute (Presov, Slovakia) and Foreign Member of the Serbian Academy of Non-linear Sciences (Belgrade, Serbia). He is the Coordinator of the PhD in Cosmology, Space Science & Space Technology (SPACE) at the Scuola Superiore Meridionale, Napoli. He is the Managing Editor of the International Journal of Geometric Methods in Modern Physics (World Scientific). He also holds research appointments at Istituto Nazionale di Fisica Nucleare (INFN), Istituto Nazionale di Astrofisica (INAF), and Gruppo Nazionale di Fisica Matematica (GNFM-INDAM). From 2012 to 2018, he was President of the Italian Society for General Relativity and Gravitation (SIGRAV). He spent periods of his scientific career in  Germany, Poland, UK, Mexico,  USA, South Africa, Canada, France, and Japan. His research focuses on general relativity, cosmology, relativistic astrophysics, and physics of gravitation in their theoretical and phenomenological aspects, in particular extended theories of gravity and their cosmological and astrophysical applications.   His main scientific achievements have been the introduction of the concept of the curvature quintessence to explain the cosmological dark energy and the use of Noether symmetries as selection rules for observable universes. In November 2023, he received the Yang-Hui Award by the ICMAACS, University of Shanghai, China.   He is the author of more than  650 refereed papers and 9 books. He is listed as one of the Top Italian Scientists.

Explains how special and general relativity are derived from basic mathematics Describes differential geometry in the simplest possible way and applies it in describing the physical world Presents Einstein’s field equations and their physical implications Provides detailed proofs