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General Relativity


Introductory Notes on fundamental concepts with derivations



Written By

Tom Brennan


Price € 30.00




About the Book:


This book is an introduction to General Relativity. It focuses on describing the tenets of General Relativity, with mathematical rigour, in the most direct way possible. No step in the development of the theory is alluded to or skipped; each is fully derived.  The core of the book is Einstein’s March 1916 paper on the foundations of his theory. The goal is to explain all steps taken in that paper. That explanation includes clarified and/or additional derivations as required and several chapters developing the mathematical tools and concepts necessary to tackle this field of study.

The work is split into two parts.

Part I, consisting of six chapters, is an introduction to the mathematics and methods. It returns to fundamental concepts, but views them with an eye to the final goal. The philosophy here is to shepherd the technical descriptions so as to maintain a focus on what is required with the minimum of digression.

Part II consists of three chapters the first, Chapter 7, gives a general overview, with some detail, of Einstein’s efforts from his first thoughts in 1907 on the topic up to his presentation of the theory in a series of lectures to the Prussian Academy in November 1915. Chapter 8 constitutes the core of this book. It concentrates on his 1916 paper, presenting and explaining the full derivations of each of the steps therein. Finally, Chapter 9 follows through on the development of the Einstein Field Equations.

Also included are eight appendices containing elaboration or further derivation, the presence of which in the main text might prove to be distractive from the primary focus.


Part I

Chapter 1 – Co-ordinates

Chapter 2 – Vectors

Chapter 3 – Dual Spaces

Chapter 4 – Transformations

Chapter 5 – Curvature

Chapter 6 – Beyond Vectors – Tensors


Part II

Chapter 7 – General Relativity Development

Chapter 8 - The Foundation of the General Theory of Relativity

Chapter 9 – Einstein's Field Equations



A1 – Lorentz Transformations

A2 - Electromagnetic Field Transformations

A3 - § 1 - Expansion of steps involved in deriving Eq. (8.3)

        § 2 - Demonstration of number of independent terms for Eq. (8.60)

A4 – Relationships concerning Newtonian gravity

A5 - Precession of the perihelion of Mercury

A6 - The Schwarzschild Metric

A7 - § 1 Energy-Momentum (Stress-Energy) Tensor

§ 2Covariant Differentiation of the Ricci Tensor,

A8 – § 1 Calculus of Variations. Technique explained

         § 2 Orthogonal Curvilinear Co-ordinates. Jacobians