The book is intended to serve as lecture material for courses on relativity at undergraduate level. Although there has been much written on special relativity the present book will emphasize the real applications of relativity. In addition, it will be physically designed with the use of box summaries so as to allow easy access of practical results. The book will be composed of eight chapters. Chapter 1 will give an introduction to special relativity that is the world without gravity. Implications will be presented with emphasis on time dilation and the Doppler shift as practical considerations. In Chapter 2, the four-vector representation of events will be introduced. The bulk of this chapter will deal with flat space dynamics. This will require the generalization of Newton's first and second laws. Some important astronomical applications will be discussed in Chapter 3 and in Chapter 4 some engineering applications of special relativity such as atomic clocks will be presented. Chapter 5 will be dedicated to the thorny question of gravity. The physical motivation of the theory must be examined and the geometrical interpretation presented. Chapter 6 will present astronomical applications of relativistic gravity. These include the usual solar system tests; light bending, time delay, gravitational red-shift, precession of Keplerian orbits. Chapter 7 will be dedicated to relativistic cosmology. Many of the standard cosmological concepts will be introduced, being mathematically simple but conceptually subtle. The concluding chapter will be largely dedicated to the global positioning system as an engineering problem that requires both inertial and gravitational relativity. The large interferometers designed as gravitational wave telescopes will be discussed here.

The book is intended to serve as lecture material for courses on relativity at undergraduate level. Although there has been much written on special relativity the present book will emphasize the real applications of relativity. In addition, it will be physically designed with the use of box summaries so as to allow easy access of practical results. The book will be composed of eight chapters. Chapter 1 will give an introduction to special relativity that is the world without gravity. Implications will be presented with emphasis on time dilation and the Doppler shift as practical considerations. In Chapter 2, the four-vector representation of events will be introduced. The bulk of this chapter will deal with flat space dynamics. This will require the generalization of Newton's first and second laws. Some important astronomical applications will be discussed in Chapter 3 and in Chapter 4 some engineering applications of special relativity such as atomic clocks will be presented. Chapter 5 will be dedicated to the thorny question of gravity. The physical motivation of the theory must be examined and the geometrical interpretation presented. Chapter 6 will present astronomical applications of relativistic gravity. These include the usual solar system tests; light bending, time delay, gravitational red-shift, precession of Keplerian orbits. Chapter 7 will be dedicated to relativistic cosmology. Many of the standard cosmological concepts will be introduced, being mathematically simple but conceptually subtle. The concluding chapter will be largely dedicated to the global positioning system as an engineering problem that requires both inertial and gravitational relativity. The large interferometers designed as gravitational wave telescopes will be discussed here.

Preface ixAcknowledgements xiIntroduction xiiiPart I: The World Without Gravity 11. Non-Relativity for Relativists 31.1 Vectors and Reference Frames 31.1.1 Reference Frames 41.1.2 Inertial Reference Frames 252. Invariance of Physical Law Under Change of Inertial Frame of Reference 452.1 Prologue 452.2 The Theory of Light or Electromagnetic Waves 482.2.1 Wave Propagation Speed 482.3 Measurement Theory and the Lorentz Transformations 623. Implications: Using and Understanding the Lorentz Transformations 793.1 Prologue 793.2 Kinematic Applications 803.2.1 Time 803.2.2 Time and Rotation 913.2.3 Time and the Lorentz Transformation 933.2.4 Space 943.2.5 Space and Time 993.3 Kinematic Acceleration 1013.3.1 Thomas Precession 1043.4 Geometrical Optics 1083.4.1 Pictures of Moving Objects 1113.4.2 Light Echoes 1184. The Measure of Space-Time 1234.1 Prologue 1234.2 Metric Space-Time 1244.2.1 Two Metric Derivations of the Lorentz Transformation 1334.3 Four-Vector Dynamics 1364.3.1 Lagrangian Dynamics Without Fundamental Forces 1404.3.2 Collisions Between Free Particles 1525. Electromagnetic Theory in Space-Time 1615.1 Prologue 1615.1.1 Electromagnetic Four-Potential 1625.2 Lagrangian Dynamics of an Electromagnetic Charge 1655.2.1 Field Transformations Between Inertial Frames 1795.3 Electromagnetism for Arbitrary Inertial Observers 1825.3.1 Curvilinear Electromagnetic Theory 192Part II: Relativity With the Gravitational Field 2036. Gravitational Structure of Space-Time 2056.1 Prologue 2056.2 The Weak Gravitational Field 2096.3 Constant or Stationary Gravitational Field 2156.4 Strong Gravitational Field 2226.4.1 The Schwarzschild Metric 2226.4.2 Orbital Precession and Light Bending in a Schwarzschild Geometry 2296.4.3 Kerr Metric Outside a Rotating Mass 2406.4.4 Relativistic Continua 2446.4.5 The Curvature of Space-Time 247Index 257