A General Relativity Workbook

Thomas A. Moore
Pomona College


CONTENTS

1 Introduction

2 Review of Special Relativity

3 Four-Vectors

4 Index Notation

5 Arbitrary Coordinates

6 Tensor Equations

7 Maxwell’s Equations

8 Geodesics

9 The Schwarzschild Metric

10 Particle Orbits

11 Precession of the Perihelion

12 Photon Orbits

13 Deflection of Light

14 Event Horizon

15 Alternative Coordinates

16 Black Hole Thermodynamics

17 The Absolute Gradient

18 Geodesic Deviation

19 The Riemann Tensor

20 The Stress-Energy Tensor

21 The Einstein Equation

22 Interpreting the Equation

23 The Schwarzschild Solution

24 The Universe Observed

25 A Metric for the Cosmos

26 Evolution of the Universe

27 Cosmic Implications

28 The Early Universe

29 CMB Fluctuations and Inflation

30 Gauge Freedom

31 Detecting Gravitational Waves

32 Gravitational Wave Energy

33 Generating Gravitational Waves

34 Gravitational Wave Astronomy

35 Gravitomagnetism

36 The Kerr Metric

37 Particle Orbits in Kerr Spacetime

38 Ergoregion and Horizon

39 Negative-Energy Orbits

Index