# Special and General Relativity

- An introduction to spacetime and gravitation

- Rainer Dick

- February 2019

### Description

This book provides a concise introduction to the special theory of relativity and the general theory of relativity. The format has been chosen to provide the basis for a single semester course that can take the students all the way from the foundations of special relativity to the core results of general relativity: the Einstein equation, and the equations of motion for particles and light in curved spacetime. To facilitate access to the topics of special and general relativity for science and engineering students, without prior training in relativity or geometry, the relevant geometric notions are introduced and developed from the ground up. Students in physics, mathematics or engineering with an interest to learn Einstein's theories of relativity should be able to use this book already in the second semester of their third year. This text might also be used as the basis of a graduate-level introduction to relativity for students who did not learn relativity as part of their undergraduate training.### About Editors

Rainer Dick studied physics at universities in Stuttgart, Karlsruhe and Hamburg, and he received a PhD from the University of Hamburg in 1990. He worked at the University of Munich, and the Institute for Advanced Study at Princeton in the USA, before joining the University of Saskatchewan in Canada, in 2000. Rainer's research interests span a wide range of topics from particle physics, cosmology and string theory, to materials physics and quantum optics. Rainer has published more than 100 papers in journals and conference proceedings, as well as the textbook*Advanced Quantum Mechanics: Materials and Photons*.

### Table of Contents

1 Why Relativity?

1.1 The Galilei invariance of Newtonian mechanics

1.2 The need for special relativity

1.3 The need for general relativity

2 A First Look at Notions from Geometry

2.1 Vectors and tensors

2.2 Curvilinear coordinates

3 The Tangents of Spacetime: Special Relativity

3.1 Lorentz transformations and the relativity of space and time

3.2 Consequences of Lorentz symmetry

3.3 The general Lorentz transformation

4 Relativistic Dynamics

4.1 Energy-momentum vectors and the relativistic Newton equation

4.2 The manifestly covariant formulation of electrodynamics

4.3 Action principles for relativistic particles

4.4 Current densities and stress-energy tensors

5 Differential Geometry: The Kinematics of Curved Spacetime

5.1 More geometry: Surfaces in R3

5.2 Covariant derivatives and Christoffel symbols

5.3 Transformations of tensors and Christoffel symbols

6 Particles in Curved Spacetime

6.1 Motion of a particle in spacetime

6.2 Slow particles in a weak gravitational field 6.3 Local inertial frames

6.4 Symmetric spaces and conservation laws

7 The Dynamics of Spacetime: The Einstein Equation

7.1 Geodesic deviation and curvature

7.2 The Einstein equation

7.3 The Schwarzschild metric

7.4 The interior of Schwarzschild black holes

7.5 Maximal extension of the Schwarzschild spacetime and wormholes

8 Massive Particles in the Schwarzschild Spacetime

8.1 Massive particles in t-independent radially symmetric spacetimes

8.2 Radial motion in terms of the effective potential

8.3 The shape of the trajectory

8.4 Clocks in the Schwarzschild spacetime

8.5 Escape velocities and infall times

9 Massless Particles in the Schwarzschild Spacetime

9.1 Equations of motion

9.2 Deflection of light in a gravitational field

9.3 Apparent photon speeds and radial infall

Index

### Bibliographic

Paperback ISBN: 9780750329675

Ebook ISBN: 9781643273792

DOI: 10.1088/2053-2571/aaf173

Publisher: Morgan & Claypool Publishers