Introduction to Relativity Volume II

E=mc² is known as the most famous but least understood equation in physics. This two-volume textbook illuminates this equation and much more through clear and detailed explanations, new demonstrations, a more physical approach, and a deep analysis of the concepts and postulates of Relativity.

Volume II contains, notably:

• In Special Relativity: complementary explanations, alternative demonstrations relying on more advanced means and revealing other aspects. Further topics: accelerated objects and the Relativistic force, nuclear reactions, the use of hyperbolic trigonometry, the Lagrangian approach, the Relativistic Maxwell’s equations.
• In General Relativity: tensors, the affine connection, the covariant derivative, the geodesic equation, the Schwarzschild solution with two of its great consequences: black holes and the bending of light; further axiomatic considerations on time, space, matter, energy and light speed.
• In Cosmology: the FLRW Metric, the Friedman equation, the cosmological constant, the four ideal cosmological Models.

These subjects are presented in a concrete and incremental manner, and illustrated by many case studies. The emphasis is placed on the theoretical aspects, with rigorous demonstrations based on a minimum set of postulates. The mathematical tools dedicated to Relativity are carefully explained for those without an advanced mathematical background.

Both volumes place an emphasis on the physical aspects of Relativity to aid the reader’s understanding and contain numerous questions and problems (147 in total). Solutions are given in a highly detailed manner to provide the maximum benefit to students.

This textbook fills a gap in the literature by drawing out the physical aspects and consequences of Relativity, which are otherwise often second place to the mathematical aspects. Its concrete focus on physics allows students to gain a full understanding of the underlying concepts and cornerstones of Relativity.

Paul Bruma is a French engineer who graduated from Institut Polytechnique - Telecom, Paris. This curriculum includes a broad program in mathematics and physics, equivalent to a Master’s degree in science.

After a career with the international telecom equipment manufacturer Alcatel-Lucent (former Bell Labs), Paul Bruma resumed physics studies, which was his favorite discipline as a student. Regarding Relativity, Paul Bruma found that most text books lack explanations and are very mathematically oriented. This explains why this subject appears quite complicated to students, and many frequently zap from one book to another in search of the missing explanations in their text books. Relativity being an essential subject, Paul Bruma took up the challenge of making a book that contains all explanations and in a manner which is as accessible as possible while always being absolutely rigorous. This induced him to adopt a more physical approach than most authors.

In his previous career in the high tech industry, Paul Bruma had many opportunities to write technical documents explaining complex subjects and to train teams. In this domain, if technical specifications are not written in a clear, detailed, step by step and unambiguous manner, the implementation teams won’t work effectively and the outcome will likely differ from what was intended. In contrast, academic authors often consider that students should fill by themselves some missing steps or explanations as part of the pedagogical process. Paul Bruma believes that this method is not the best one for Relativity because it is a domain where common sense often misleads.