Introduction To General Relativity

by John Dirk Walecka

Overview

A working knowledge of Einstein's theory of general relativity is an essential tool for every physicist today. This self-contained book is an introductory text on the subject aimed at first-year graduate students, or advanced undergraduates, in physics that assumes only a basic understanding of classical Lagrangian mechanics. The mechanics problem of a point mass constrained to move without friction on a two-dimensional surface of arbitrary shape serves as a paradigm for the development of the mathematics and physics of general relativity. After reviewing special relativity, the basic principles of general relativity are presented, and the most important applications are discussed. The final special topics section guides the reader through a few important areas of current research.This book will allow the reader to approach the more advanced texts and monographs, as well as the continual influx of fascinating new experimental results, with a deeper understanding and sense of appreciation.

Product Details

ISBN-13:	9789812705846
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	04/20/2007
Edition description:	New Edition
Pages:	356
Product dimensions:	6.10(w) x 9.10(h) x 0.90(d)

Table of Contents

Preface     vii
Introduction     1
Particle on a Two-Dimensional Surface     9
Infinitesimal Displacements     10
Lagrange's Equations     12
Reciprocal Basis     14
Geodesic Motion     19
Role of Coordinates     24
Curvilinear Coordinate Systems     27
Line Element     27
Reciprocal Basis     29
Metric     29
Vectors     30
Tensors     31
Change of Basis     33
Transformation Law     36
Affine Connection     39
Example: Polar Coordinates     41
Particle on a Two-Dimensional Surface-Revisited     43
Motion in Three-Dimensional Euclidian Space     43
Parallel Displacement     46
Some Tensor Analysis     51
Covariant Derivative     51
The Riemann Curvature Tensor     54
Second Covariant Derivative     60
Covariant Differentiation     64
Symmetry Properties of the Riemann Tensor     67
Bianchi Identities     68
The Einstein Tensor     69
Example-Surface of a Sphere     72
Volume element     76
Special Relativity     87
Basic Principles     87
Four-Vectors     88
Relativistic Particle Motion     91
Lorentz Transformations     98
General Tensor Transformation Law     109
Relativistic Hydrodynamics     111
Transition to General Relativity     120
General Relativity     123
Einstein's Theory     123
Newtonian Limit     126
The Equivalence Principle     131
Local Freely Falling Frame (LF[superscript 3])     133
Spherically Symmetric Solution to Field Equations     135
Solution in Vacuum     143
Interpretation of Schwarzschild Metric     148
A Few Applications     152
Precession of Perihelion     155
Lagrangian     156
Equations of Motion     159
Equilibrium Circular Orbits     163
Small Oscillations About Circular Orbits     164
Some Numbers and Comparison with Experiment     169
Deflection of Light     171
Gravitational Redshift     173
Basic Observation     174
Frequency Shift      174
Propagation of Light     176
A Cyclic Process     178
Neutron Stars     181
Hydrodynamics in General Relativity     181
Tolman-Oppenheimer-Volkoff (TOV) Equations     190
Relativistic Mean Field Theory of Nuclear Matter (RMFT)     201
Neutron Stars and Black Holes     210
Cosmology     217
Uniform Mass Background     218
Robertson-Walker Metric with k = 0     220
Solution to Einstein's Equations     225
Interpretation     229
Cosmological Redshift     233
Horizon     237
Some Comments     239
Gravitational Radiation     241
Linearized Theory     241
Auxiliary (Lorentz) Condition     245
Plane-Wave Solution to the Einstein Field Equations     250
Interpretation     253
Detection     257
Special Topics     263
Einstein-Hilbert Lagrangian     264
Cosmological Constant     267
Additional Scalar Field     268
Robertson-Walker Metric with k [not equal] 0     270
Inflation     275
Problems     281
Reduction of g[superscript mu nu delta]R[subscript mu nu] to covariant divergences     321
Robertson-Walker Metric with k [not equal]     325
Bibliography     327
Index     331