Part I – Introduction and Fundamental Structure
1 Introduction
The general theory of relativity, published in 1915 by Albert Einstein, forms one of the cornerstones of our modern understanding of space, time, and gravity. This theory replaces Newton’s classical model of gravity with an elegant geometric picture: mass and energy curve spacetime, and objects follow the curvature of that spacetime, a concept with profound implications for both fundamental physics and cosmology.
1.1 Purpose of this document
The purpose of this document is to provide an overview of general relativity, with emphasis on:
- A careful derivation of the mathematical structure underlying the theory.
- An examination of practical applications and experiments that support the theory.
- Addressing frequently asked questions about concepts and formulas within general relativity.
1.2 Approach
The approach in this document differs from popular descriptions. We focus on:
- Thorough derivations of tensor-analytic equations.
- A careful treatment of coordinate transformations.
- Application of the Schwarzschild solution to classical experiments such as the Hafele–Keating experiment (with careful attention to the approximation used), the deflection of light by gravity, and the precession of Mercury.
We also demonstrate that the Schwarzschild solution satisfies Einstein’s field equations, and how spacetime curvature is expressed mathematically in terms of the metric and Christoffel symbols.
1.3 Intended audience
This document is written for:
- (Geo)physicists and mathematicians interested in the underlying structure of general relativity.
- Physics students who want to go beyond standard textbooks.
- Anyone who wants to understand why the equations are the way they are, not just how they work.
1.4 Final remarks
This document is structured so that each chapter builds on the previous one, but where possible, sections can also be read independently. The appendices provide additional explanations, alternative derivations, and applications in the context of special relativity and nuclear physics.