Relativistically Speaking: An Introduction to General Relativity (Fiat Lux)

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 an 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.