Relativistically Speaking: An Introduction to General Relativity (Fiat Lux Book 2) by Naveen Balaji Umasankar (PDF)

Description

This book lays the mathematical foundations to General Relativity (GR) and presents the majestic grandeur and essence of the theory in a new and contemporary style. The aim of this book is to present with precision, but as intuitively as possible, the foundations and main consequences of GR and it is written for students of physics interested in exact mathematical formulations or for students of mathematics interested in intuitive understanding of physics. The six chapters of the book cover a wide range of topics, discussing in detail Spacetime mathematics, Einstein’s field equations, the Schwarzschild solution and advanced concepts such as the Petrov Classification, the Kulkarni-Nomizu product, the Weyl-Schouten theorem, embedding mechanisms like the Fujitani-Ikeda-Matsumoto embedding, and the Schwarzschild-Tangherlini metric. A complete chapter has been dedicated to the study of singularities and their eliminations. The book aims at communicating the concepts as intuitively as possible, constantly promoting the avant-garde and consciously avoiding the vicissitudes one faces in the conventionalist approach to physics and the labyrinthine choice of words in archaic texts. Each chapter includes a wide array of examples that motivate the reader to solve the exercises thus, providing a holistic understanding.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is an absolutely excellent book for a grad student like myself. It firmly establishes many elements and fundamentals of the theory with solid reasoning and mathematics.It is to be noted that a bit of knowledge of sets and manifolds may be good to have a priori to reading the book, although the initial chapter on the ‘essential mathematics’ firmly establishes a foundation to start with. The latter chapters are mathematically rigorous, but the rigor is built at a uniform pace via very elucidative texts. The six chapters provide an excellent (graduate level) coverage of the main GR topics. Chapter 5 provides extensive coverage of the embedding machinery and rare-to-access-topics such as the Fujitani embedding techniques. Chapter 6, named ‘Advanced Topics’ provides a detailed description of the Penrose classification and Causality theory (this is something which has been developed throughout the book in multiple digestible parts).The chapter on the Field equations of Einstein is very accessible in the way it has been written and presented. The chapter first builds intuition behind the need for the equations and later provides an excellent description of the meaning of conservation and how the same is linked to continuity (this is done via some great artwork). A brief introduction to the Lagrangian formulation is given (and hence, no mastery of Classical Mechanics is presumed), and finally the Field equations are derived by varying the Einstein-Hilbert action in a step-by-step manner (something which I really liked). This book deals with black holes in a unique fashion, dedicating three chapters to the same-one which deals with the standard Schwarzschild black hole, and the others which cover a wide range of topics which include theorems such as Birkhoff’s, Israel’s and Price’s, and Killing horizons.This is a truly unique presentation of GR and the material is presented in a way that is intuitive without compromising mathematical rigor. I would recommend following other standard books such as MTW or Wald (just to name a few) in parallel to completely grasp and master GR.

⭐This is a really well written book.I was a part of the GR summer course which basically covered everything from this book.Helped a lot!

⭐

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