General Relativity

An Introduction to Curved Spacetime

This book is a lucid and concise introduction to general relativity, written by a tiny spacetime bug who inhabits the four-dimensional spacetime. Knowing every corner of its environment, the bug loves to share with you what it has learned and understood about this marvelous theory, which represents humans' latest understanding about space, time, and motion.

General relativity is a cornerstone of modern physics. At present, it stands proudly alongside quantum mechanics. If you want to look far and deep into the universe, and learn about its wonders and mysteries, you need a knowledge of this theory.

This is an intellectual journey that cannot be missed.


Hello !

I'm a bug that lives in the 4-dimensional spacetime.

General relativity represents humans' latest understanding about space, time, and motion at the macroscopic scale. It is used for the study of black holes and the universe itself. Yes, our vast universe is full of wonders and mysteries.

But the microscopic picture of gravity is still an open question. So much is known about general relativity, but so much more remains unknown, to be discovered.

If you want to understand general relativity, join me! I have been through all the difficulties that may be encountered while learning the theory. This book is a deep, lucid, and the most insightful introduction to the theory.

Unlike most other books, this book presents the physical principles of the theory as well as the relevant mathematical techniques in a direct, careful, and profound manner. At the end of the journey, you'll have acquired a deep understanding of general relativity.

The book shows all calculations in complete detail. It also contains exercises with full solutions provided.


Goals

In simple and direct language, I will guide you gently and thoroughly through the physical ideas and mathematical techniques of this wonderful theory. Join me in this journey to one of the frontiers of human knowledge, at the end of which you will:

  • Understand intuitively and uniquely the physical ideas of general relativity.
  • Acquire a deep understanding of the mathematics of curved spacetime, or Riemannian geometry, and be able to truly appreciate its beauty.
  • Be able to calculate motions of objects in flat and curved spacetimes.
  • Understand black holes and how general relativity is used to study our vast and fascinating universe.

Contents

Introduction

From Newton to Einstein

Chapter 1

The Problem of Gravity

Chapter 2

Newtonian Gravity

Chapter 3

Special Relativity

Chapter 4

Flat and Curved Spaces

Chapter 5

The Geometry of Spacetime

Chapter 6

The Einstein Field Equations

Chapter 7

Black Holes

Chapter 8

Cosmology

End

Some Closing Words