UNITEXT for Physics

A Mathematical Journey to Relativity

Deriving Special and General Relativity with Basic Mathematics

Authors: Boskoff, Wladimir-Georges, Capozziello, Salvatore

Free Preview
  • 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 
see more benefits

Buy this book

eBook 71,68 €
price for Spain (gross)
  • ISBN 978-3-030-47894-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 88,39 €
price for Spain (gross)
About this Textbook

This book opens with an axiomatic description of Euclidean and non-Euclidean geometries. Euclidean geometry is the starting point to understand all other geometries and it is  the cornerstone for our basic intuition of vector spaces. The generalization to non-Euclidean geometry is the following step to develop the language of Special and General Relativity.  These theories are discussed starting from a full geometric point of view. Differential geometry is presented in the simplest  way and it is applied to describe the physical world. The final result of this construction is deriving the Einstein field equations for gravitation and spacetime dynamics. Possible solutions, and their physical implications are also discussed: the Schwarzschild metric, the relativistic trajectory of planets, the deflection of light, the black holes, the cosmological solutions like de Sitter, Friedmann-Lemaître-Robertson-Walker, and Gödel ones. Some current problems like dark energy are also scketched. The book is   self-contained and includes details of all proofs. It provides solutions  or tips to  solve problems and exercises. It is designed for undergraduate students and for all readers who want a first geometric approach to Special and General Relativity.

About the authors

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 a Full Professor of Astronomy and Astrophysics at the Department of Physics at the Universita'  di Napoli "Federico II", Visiting Professor at Gran Sasso Science Institute (L'Aquila), and Honorary Professor at Tomsk State Pedagogical University (Russia). 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). Professor Capozziello has spent periods of his scientific career in  Germany, Poland, the UK, Mexico, the 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 achievement has been in 2002 when he introduced the concept of gravitational curvature quintessence, f(R) gravity, to explain the cosmological dark energy. He is the author of almost 550 refereed papers and six books and listed as one of the Top Italian Scientists.

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook 71,68 €
price for Spain (gross)
  • ISBN 978-3-030-47894-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 88,39 €
price for Spain (gross)
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
A Mathematical Journey to Relativity
Book Subtitle
Deriving Special and General Relativity with Basic Mathematics
Authors
Series Title
UNITEXT for Physics
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-47894-0
DOI
10.1007/978-3-030-47894-0
Hardcover ISBN
978-3-030-47893-3
Series ISSN
2198-7882
Edition Number
1
Number of Pages
XXII, 397
Number of Illustrations
38 b/w illustrations, 6 illustrations in colour
Topics