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An Introduction to Relativistic Gravitation - Remi Joel Hakim

An Introduction to Relativistic Gravitation

By: Remi Joel Hakim, Andrew King (Translator)


Published: 19th July 1999
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This is an introductory textbook on applications of general relativity to astrophysics and cosmology. The aim is to provide graduate students with a toolkit for understanding astronomical phenomena that involve velocities close to that of light or intense gravitational fields. The approach taken is first to give the reader a thorough grounding in special relativity, with space-time the central concept, following which general relativity presents few conceptual difficulties. Examples of relativistic gravitation in action are drawn from the astrophysical domain. The book can be read on two levels: first as an introductory fast-track course, and then as a detailed course reinforced by problems which illuminate technical examples. The book has extensive links to the literature of relativistic astrophysics and cosmology.

'This textbook offers a thorough application of relativity theory to astrophysics and modern cosmology ... the reviewer found Hakim's descriptions both useful and clear and a well-ordered progression of the material has been presented ... Hakim's text must rank amongst the best of them.' A. D. Andrews, Irish Astronomical Journal

Prefacep. xi
Newtonian Gravitationp. 1
Newtonian space-timep. 1
Simultaneity and distance measuresp. 4
Newton's absolutes and the notion of the etherp. 7
The principle of inertiap. 9
The laws of dynamics and Galilean relativityp. 12
Inertia and relativity principles as seen by Galileop. 16
Newtonian gravitationp. 17
Measuring the gravitational constantp. 22
Limits of the Newtonian theory of gravityp. 28
The finiteness of the velocity of lightp. 30
Michelson's experimentp. 34
Minkowski Space-Timep. 41
The space-time of special relativityp. 43
The Lorentz transformationp. 46
Remarksp. 48
Causality and simultaneityp. 52
Times and distances measured by inertial observersp. 58
Global properties of space-timep. 60
Experimental verification of Special Relativityp. 61
The Relativistic Form of Physical Lawsp. 68
Tensor formalismp. 68
The Doppler effect and aberrationp. 75
The kinematic description of particle motionp. 77
Relativistic dynamics: E=mc[superscript 2]p. 82
Minkowski space in curvilinear coordinatesp. 85
Gravitation and Special Relativityp. 95
The gravitational redshiftp. 97
Light bendingp. 98
The advance of the perihelion of Mercuryp. 99
The need for nonlinear equations for gravitationp. 101
Electromagnetism and Relativistic Hydrodynamicsp. 103
Densities and currentsp. 103
The equations of electromagnetismp. 106
The energy-momentum tensorp. 109
Relativistic hydrodynamicsp. 110
What is Curved Space?p. 116
Some manifestations of curvaturep. 116
Curvature of two-dimensional surfacesp. 119
The meaning of intrinsic curvaturep. 125
Surfaces in R[superscript n] - Riemann spacesp. 126
Intrinsic curvature of a manifoldp. 129
Properties of the curvature tensorp. 130
Space-time as a Riemannian manifoldp. 132
Some properties of tensors in curved spacep. 133
Three arguments for curved space-timep. 134
The Principle of Equivalencep. 139
The weak equivalence principle and the Eotvos-Dicke experimentsp. 140
The equivalence principle and minimal couplingp. 149
The gravitational redshiftp. 157
Geodesic motionp. 159
Geodesic deviationp. 162
The metric tensor in spherical symmetryp. 163
Overview of the PPN formalismp. 165
The classical testsp. 167
Gravitational lensesp. 174
Einstein's Relativistic Gravitation (General Relativity)p. 187
Einstein's equationsp. 188
Other derivations of the Einstein equationsp. 192
The Schwarzschild solutionp. 195
The local geometry of Friedman spacesp. 200
Other metrics of astrophysical interestp. 206
The linearised Einstein equationsp. 207
Gravitational radiationp. 210
Tensorsp. 227
Dual of a vector spacep. 227
Tensor products of vector spacesp. 228
Criteria for being a tensorp. 229
Exterior Differential Formsp. 232
Exterior calculusp. 234
Differential formsp. 236
Volume element: dual formsp. 238
Differentiation of formsp. 241
Maxwell's equations in differential formsp. 242
Integration of differential forms - Stokes' theoremp. 243
Variational Form of the Field Equationsp. 245
The Concept of a Manifoldp. 249
Differentiable manifoldsp. 252
Referencesp. 255
Physical Constantsp. 270
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521459303
ISBN-10: 0521459303
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 271
Published: 19th July 1999
Country of Publication: GB
Dimensions (cm): 23.39 x 15.72  x 1.42
Weight (kg): 0.49