This book is based on a set of 18 class-tested lectures delivered to fourth-year physics undergraduates at Griffith University in Brisbane, and the book presents new discoveries by the Nobel-prize winning LIGO collaboration. The author begins with a review of special relativity and tensors and then develops the basic elements of general relativity (a beautiful theory that unifies special relativity and gravitation via geometry) with applications to the gravitational deflection of light, global positioning systems, black holes, gravitational waves, and cosmology. The book provides readers with a solid understanding of the underlying physical concepts; an ability to appreciate and in many cases derive important applications of the theory; and a solid grounding for those wishing to pursue their studies further.
General Relativity: An Introduction to Black Holes, Gravitational Waves, and Cosmology also connects general relativity with broader topics. There is no doubt that general relativity is an active and exciting field of physics, and this book successfully transmits that excitement to readers.
Table of Contents
1 Concepts in special relativity
1.1 Galilean relativity
1.2 Inertial frames
1.3 Special relativity
1.4 Velocity addition, length contraction and time dilation
1.5 Questions
2 Tensors in relativity
2.1 Motivation
2.2 General tensors and their basic properties
2.3 Lorentz tensors
2.4 Example: 4-momentum and force
2.5 Example: Doppler effect
2.6 Questions
3 The equivalence principle and local inertial frames
3.1 Inertial vs gravitational mass
3.2 Einstein’s equivalence principle
3.3 Local inertial frames
3.4 Questions
4 The motion of freely falling particles in general relativity
4.1 Local inertial frames and the geodesic equation
4.2 The metric tensor
4.3 Gravity as geometry
4.4 The Newtonian limit
4.5 Questions
5 The Schwarzschild metric and black holes
5.1 Spherical symmetry and the Schwarzschild metric
5.2 Geodesics in spherically symmetric spacetimes
5.3 Particle geodesics in a Schwarzschild spacetime
5.4 Deflection of light by the sun
5.5 Falling into a black hole
5.6 Questions
6 Tensors and geometry
6.1 Covariant derivatives
6.2 Basic properties of covariant derivatives
6.3 Riemann and Ricci tensors
6.4 Symmetries and Bianchi identities
6.5 Questions
7 Einstein’s field equations
7.1 Overview
7.2 Energy-momentum tensor and conservation laws
7.3 The field equations for general relativity
7.4 The cosmological constant
7.5 Questions
8 Solving the field equations: vacuum solutions
8.1 The vacuum equations
8.2 The Schwarzschild-deSitter solution
8.3 Gravitational waves
8.4 Questions
9 Solving the field equations: cosmological solutions
9.1 The cosmological principle
9.2 The Friedmann-Robertson-Walker metric
9.3 Friedmann-Robertson-Walker universes
9.4 Questions
A Derivation of Lorentz transformations
B Derivation of Einstein’s field equations
C Remarks on selected questions
About the Author(s)
Michael J.W. Hall, Griffith University, Australia
Michael Hall, PhD, received PhD from the Australian National University in 1989. Since then he has worked in various areas of the foundations of physics, from both inside and outside academia (including a year as a Humboldt Fellow in Ulm, and sixteen as a patent examiner). For the last six years he has been a research fellow in the Centre for Quantum Dynamics at Griffith University in Brisbane and has recently taken up a visiting fellowship at the Australian National University in Canberra.
Dr. Hall’s research interests include quantum optics and information, time observables, quantum locality, relativistic Hamiltonians, the consistent coupling of classical spacetime to quantum matter, and the many-interacting-worlds approach to quantum mechanics. He is a member of the editorial boards of the Journal of Physics A and Physical Review A.
Related Series
General and Introductory Physics
