Exact solutions and scalar fields in gravity: recent developments

✍ Scribed by Alfredo Macías, Jorge Luis Cervantes Cota, Claus Lämmerzahl, Editors

• Publisher: Springer
• Year: 2001
• Tongue: English
• Leaves: 353
• Edition: 1
• Category: Library

✦ Synopsis

Divided into four parts, this book covers recent developments in topics pertaining to gravity theories, including discussions on the presence of scalar fields. Part One is devoted to exact solutions in general relativity, and is mainly concerned with the results of rotating null dust beams and fluids. Also included is a panoramic vision of new research directions in this area, which would require revising certain theorems and their possible extensions within gravity theories, new aspects concerning the Ernst potentials, double Kerr spacetimes, and rotating configurations. In particular, there is a detailed discussion of totally symmetric and totally geodesic spaces, in which a method for generating (2+1)-dimensional solutions from (3+1)-dimensional solutions is given. Part Two deals with alternative theories of gravity, all of which include scalar fields and gauge fields. Here, quantum and cosmological effects, which arise from both gravity theories in four and higher dimensions and from metric-affine theories, are investigated. Part Three is devoted to cosmological and inflationary scenarios. Local effects, such as the influence of scalar fields in protogalactic interactions, numerical studies of the collapse of molecular cores, as well as the inverse inflationary problem and the blue eigenvalue spectrum of it, are considered. Moreover, the role of scalar fields as dark matter and quantum cosmology in the Bergman-Wagoner and Gowdy theories, together with the relation of the conformal symmetry and deflationary gas universe, are likewise presented. The last part of the book includes some mixed topics which are still in the experimental stage. Among them are the foundation of the Maxwell theory, a discussion on electromagnetic Thirring problems, a note on the staticity of black holes with non-minimally coupled scalar fields, and a study of the Lorentz force free charged fluids in general relativity. Thus, this book is the most up-to-date, comprehensive collection of papers on the subject of exact solutions and scalar fields in gravity and is a valuable tool for researchers in the area.

✦ Table of Contents

Contents......Page 8
Preface......Page 16
Contributing Authors......Page 18
Part I Exact Solutions......Page 26
1 Newtonian configurations......Page 28
2 Dirichlet boundary problem vs. free-boundary problem......Page 31
3 Interior solutions with differential rotation in general relativity......Page 32
4 Vacuum as a “perfect fluid”. The “rigid rotation” and the “irrotational” gauges......Page 35
5 Some geometric features of a rigidly rotating perfect fluid interior solution......Page 37
1 Introduction......Page 40
2 The Quest for the Geroch Group and its Generalizations......Page 41
3 The Perfect Fluid Joining Problem......Page 43
4 Future Directions......Page 44
5 Time for a New World Order?......Page 45
1 Introduction......Page 48
2 Killing Equations and Integrability Conditions......Page 49
3 Maximally Symmetric Spaces......Page 51
4 Representation of Maximally Symmetric Spaces......Page 54
5 Maximally Symmetric Sub–spaces......Page 56
6 Totally Geodesic Hypersurfaces......Page 57
7 Totally Geodesic Sub–spaces......Page 60
8 The 2+1 BTZ Solution as Hypersurface of the 3+1 PC Metric......Page 61
1 The theta formula for the Ernst potential......Page 64
2 Calculation of the arguments......Page 67
3 Transformation of the theta formula......Page 73
5 Appendix......Page 75
1 Introduction......Page 78
2 The superposition of spherically symmetric beams of null dust......Page 80
3 The gravitational field of two counter–moving beams of light......Page 81
4 Discussion......Page 85
2 A short history of the problem......Page 88
3 A new approach to the double–Kerr equilibrium problem......Page 89
4 The Komar masses and angular momenta......Page 91
5 Towards the analysis of the multi–black hole equilibrium states......Page 92
1 Figures of equilibrium of rotating fluid masses......Page 94
2 Rotating dust configurations – The Maclaurin disk......Page 96
3 General–relativistic continuation......Page 97
4 Black–hole limit......Page 99
5 Discussion......Page 100
1 Introduction......Page 102
2 Nonlocal conservation laws......Page 104
3 Linear systems for ME......Page 105
4 Twistor construction......Page 107
5 The case of Θ = ∑[sup(∞)][sub(k=−N<0)]ħ[sup(k)]Θ[sub(k)]......Page 109
Part II Alternative Theories and Scalar Fields......Page 114
1 Introduction......Page 116
2 Barotropic Fluids......Page 118
3 Radiation......Page 120
4 Vacuum......Page 122
5 Conclusions......Page 123
1 Higgs–field gravity......Page 126
2 Higgs–field scalar tensor theory of gravity......Page 130
The road to Gravitational S–duality......Page 136
1 Introduction......Page 137
2 S–Duality in Topological Gravity......Page 138
3 S–Duality in MacDowell–Mansouri Gauge Theory of Gravity......Page 141
4 (Anti)Self–duality of the Three–dimensional Chern–Simons Gravity......Page 144
5 ChernSimons Gravity Dual Action in Three Dimensions......Page 145
6 Concluding Remarks......Page 146
1 Introduction......Page 148
2 The model......Page 149
3 Toda–type solutions from null–geodesic method......Page 151
4 Cosmological solutions......Page 153
5 Black hole solutions......Page 154
6 Post–Newtonian approximation......Page 155
1 Introduction......Page 158
2 Chern–Simons action in five dimensions......Page 159
3 Five dimensional principal fiber boundle......Page 161
4 Effective action......Page 162
5 Discussion......Page 165
1 Introduction......Page 166
2 MAG in general......Page 167
3 The triplet ansatz......Page 169
4 Plane–fronted waves in GR......Page 170
5 Plane-fronted waves in MAG......Page 173
6 Summary......Page 176
Part III Cosmology and Inflation......Page 178
1 Introduction......Page 180
2 Equations for FRW and Bianchi models......Page 181
3 Solutions and asymptotic behavior in BD theory......Page 183
4 Conclusions......Page 187
Scalar Field Dark Matter......Page 190
1 Introduction......Page 191
2 Cosmological Scalar Field Solutions......Page 193
3 Scalar dark matter and Planck scale physics......Page 199
4 Spherical Scalar Field Fluctuations as Galactic Halos......Page 201
5 The Galaxy Center......Page 206
6 Conclusions......Page 207
1 Introduction......Page 210
2 Spatially flat inflationary universe......Page 212
3 Abel equation from second-order slow–roll approximation......Page 213
4 Complete eigenvalue spectrum......Page 215
5 Discussion......Page 217
1 Introduction......Page 220
2 Isotropic models......Page 221
3 Anisotropic models......Page 225
4 Final remarks......Page 227
1 Introduction......Page 230
2 Gowdy T[Sup(3)] Cosmological Models......Page 231
3 Analogies and general results......Page 233
4 The Big Bang......Page 235
1 Introduction......Page 238
2 Scalar Fields and the Newtonian Approximation......Page 240
3 Protogalactic Cloud Models and Results......Page 241
4 Conclusions......Page 245
1 Introduction......Page 248
2 Initial Model and Computational Methods......Page 250
3 Results......Page 253
4 Conclusions......Page 257
1 Introduction......Page 260
2 The standard formulas......Page 261
3 Generalizing the Bessel approximation......Page 266
4 Testing the expressions......Page 269
5 Conclusions......Page 270
1 Introduction......Page 272
2 Fluid description......Page 274
3 Gas dynamics......Page 275
4 Cosmological dynamics and conformal symmetry......Page 277
5 Phenomenological vacuum decay......Page 280
6 Equivalent scalar field dynamics......Page 281
7 Conclusions......Page 282
Part IV Experiments and Other Topics......Page 286
1 Introduction......Page 288
2 The Staticity Theorem for Non–MinimallyCoupled Scalar Fields......Page 290
3 Conclusions......Page 294
1 Introduction......Page 296
2 Yukawa term......Page 298
3 Quantum Measurements......Page 299
4 Quantum nondemolition measurements......Page 300
5 QND and non–Newtonian gravity: Propagators and probabilities......Page 301
6 Conclusions......Page 302
1 Introduction......Page 306
2 The Static Two–Shell Model......Page 307
3 First Order Rotation of the Shells......Page 310
4 Results......Page 313
1 Introduction......Page 320
2 Quantum gravity inspired modification of Maxwell’s equations......Page 321
3 Tests of Maxwell’s equations......Page 324
4 Laboratory Tests......Page 325
5 Astrophysical observations......Page 328
6 Conclusion......Page 332
1 Introduction......Page 336
2 LFFS in general relativity......Page 339
3 The ansatz of zero Lorentz force in special relativistic electro-dynamics......Page 342
4 Conclusions......Page 343
I......Page 346
T......Page 347
Y......Page 348