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A Mathematical Journey to Relativity - Deriving Special and General Relativity with Basic Mathematics (Paperback, 1st ed. 2020)
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A Mathematical Journey to Relativity - Deriving Special and General Relativity with Basic Mathematics (Paperback, 1st ed. 2020)
Series: UNITEXT for Physics
Expected to ship within 10 - 15 working days
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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-Lemaitre-Robertson-Walker, and Goedel 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.
General
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