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The Mathematical Theory of Cosmic Strings : Cosmic Strings in the Wire Approximation - Malcolm R. Anderson

The Mathematical Theory of Cosmic Strings

Cosmic Strings in the Wire Approximation

Hardcover Published: 18th November 2002
ISBN: 9780750301602
Number Of Pages: 380

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This book is a comprehensive survey of the current state of knowledge about the dynamics and gravitational properties of cosmic strings treated in the idealized classical approximation as line singularities described by the Nambu-Goto action. The author's purpose is to provide a standard reference to all work that has been published since the mid-1970s and to link this work together in a single conceptual framework and a single notational formalism. A working knowledge of basic general relativity is assumed. The book will be essential reading for researchers and postgraduate students in mathematics, theoretical physics, and astronomy interested in cosmic strings.

Industry Reviews

"Anderson provides a comprehensive summary and review of the mathematical theory of cosmic strings. The subject is not in a state of rapid change so the book is up to date and it is likely to remain so for some time. Although the book is technical and requires a strong mathematical background and an interest in differential geometry, it is well written and reads easily . . . I found the later sections particularly interesting, especially the discussion of the infinite straight string and the associated singularity structure . . . This is a valuable reference work and compendium of results." -- D R Matravers, Comtemporary Physics, 2003, 44/5

Introductionp. ix
Cosmic strings and broken gauge symmetriesp. 1
Electromagnetism as a local gauge theoryp. 3
Electroweak unificationp. 8
The Nielsen--Olesen vortex stringp. 15
Strings as relics of the Big Bangp. 24
The Nambu actionp. 27
The elements of string dynamicsp. 35
Describing a zero-thickness cosmic stringp. 35
The equation of motionp. 38
Gauge conditions, periodicity and causal structurep. 41
Conservation laws in symmetric spacetimesp. 44
Invariant lengthp. 48
Cusps and curvature singularitiesp. 49
Intercommuting and kinksp. 54
String dynamics in flat spacep. 59
The aligned standard gaugep. 59
The GGRT gaugep. 61
Conservation laws in flat spacep. 63
Initial-value formulation for a string loopp. 68
Periodic solutions in the spinor representationp. 70
The Kibble--Turok sphere and cusps and kinks in flat spacep. 73
Field reconnection at a cuspp. 80
Self-intersection of a string loopp. 85
Secular evolution of a string loopp. 92
A bestiary of exact solutionsp. 99
Infinite stringsp. 99
The infinite straight stringp. 99
Travelling-wave solutionsp. 100
Strings with paired kinksp. 102
Helical stringsp. 103
Some simple planar loopsp. 105
The collapsing circular loopp. 105
The doubled rotating rodp. 106
The degenerate kinked cuspless loopp. 107
Cat's-eye stringsp. 108
Balloon stringsp. 112
Harmonic loop solutionsp. 114
Loops with one harmonicp. 114
Loops with two unmixed harmonicsp. 117
Loops with two mixed harmonicsp. 122
Loops with three or more harmonicsp. 127
Stationary rotating solutionsp. 130
Three toy solutionsp. 135
The teardrop stringp. 135
The cardioid stringp. 137
The figure-of-eight stringp. 141
String dynamics in non-flat backgroundsp. 144
Strings in Robertson--Walker spacetimesp. 144
Straight string solutionsp. 145
Ring solutionsp. 147
Strings near a Schwarzschild black holep. 152
Ring solutionsp. 153
Static equilibrium solutionsp. 157
Scattering and capture of a straight string by a Schwarzschild holep. 159
Ring solutions in the Kerr metricp. 167
Static equilibrium configurations in the Kerr metricp. 170
Strings in plane-fronted-wave spacetimesp. 177
Cosmic strings in the weak-field approximationp. 181
The weak-field formalismp. 182
Cusps in the weak-field approximationp. 185
Kinks in the weak-field approximationp. 189
Radiation of gravitational energy from a loopp. 191
Calculations of radiated powerp. 196
Power from cuspless loopsp. 197
Power from the Vachaspati--Vilenkin loopsp. 199
Power from the p/q harmonic solutionsp. 202
Power radiated by a helical stringp. 204
Radiation from long stringsp. 208
Radiation of linear and angular momentump. 211
Linear momentump. 211
Angular momentump. 213
Radiative efficiencies from piecewise-linear loopsp. 219
The piecewise-linear approximationp. 219
A minimum radiative efficiency?p. 223
The field of a collapsing circular loopp. 226
The back-reaction problemp. 231
General features of the problemp. 231
Self-acceleration of a cosmic stringp. 234
Back-reaction and cusp displacementp. 240
Numerical resultsp. 242
The gravitational field of an infinite straight stringp. 246
The metric due to an infinite straight stringp. 246
Properties of the straight-string metricp. 250
The Geroch--Traschen critiquep. 252
Is the straight-string metric unstable to changes in the equation of state?p. 255
A distributional description of the straight-string metricp. 259
The self-force on a massive particle near a straight stringp. 263
The straight-string metric in 'asymptotically-flat' formp. 267
Multiple straight strings and closed timelike curvesp. 271
Straight strings and 2 + 1 gravityp. 271
Boosts and rotations of systems of straight stringsp. 273
The Gott constructionp. 274
String holonomy and closed timelike curvesp. 278
The Letelier--Gal'tsov spacetimep. 282
Other exact string metricsp. 286
Strings and travelling wavesp. 286
Strings from axisymmetric spacetimesp. 291
Strings in a Robertson--Walker universep. 292
A string through a Schwarzschild black holep. 297
Strings coupled to a cosmological constantp. 301
Strings in radiating cylindrical spacetimesp. 303
The cylindrical formalismp. 303
Separable solutionsp. 305
Strings in closed universesp. 307
Radiating strings from axisymmetric spacetimesp. 310
Einstein--Rosen soliton wavesp. 316
Two-mode soliton solutionsp. 321
Snapping cosmic stringsp. 324
Snapping strings in flat spacetimesp. 324
Other spacetimes containing snapping stringsp. 329
Strong-field effects of zero-thickness stringsp. 332
Spatial geometry outside a stationary loopp. 334
Black-hole formation from a collapsing loopp. 340
Properties of the near gravitational field of a cosmic stringp. 343
A 3 + 1 split of the metric near a cosmic stringp. 346
General formalismp. 346
Some sample near-field expansionsp. 349
Series solutions of the near-field vacuum Einstein equationsp. 352
Distributional stress--energy of the world sheetp. 355
Bibliographyp. 359
Indexp. 367
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780750301602
ISBN-10: 0750301600
Series: High Energy Physics, Cosmology and Gravitation
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 380
Published: 18th November 2002
Country of Publication: GB
Dimensions (cm): 24.03 x 15.95  x 2.59
Weight (kg): 0.79
Edition Number: 1

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