search for books and compare prices
Tables of Contents for Exact Solutions and Scalar Fields in Gravity
Chapter/Section Title
Page #
Page Count
Preface
xv
Contributing Authors
xvii
Part I Exact Solutions
Self-gravitating stationary axi-symmetric perfect fluids: Differential rotation and some geometric features
3
12
F.J. Chinea
Newtonian configurations
3
3
Dirichlet boundary problem vs. free-boundary problem
6
1
Interior solutions with differential rotation in general relativity
7
3
Vacuum as a ``perfect fluid''. The ``rigid rotation'' and the ``irrotational'' gauges
10
2
Some geometric features of a rigidly rotating perfect fluid interior solution
12
3
New Directions for the New Millennium
15
8
Frederick J. Ernst
Introduction
15
1
The Quest for the Geroch Group and its Generalizations
16
2
The Perfect Fluid Joining Problem
18
1
Future Directions
19
1
General
19
1
Radiating Axisymmetric Systems
20
1
Time for a New World Order?
20
3
On maximally symmetric and totally geodesic spaces
23
16
Alberto Garcia
Introduction
23
1
Killing Equations and Integrability Conditions
24
2
Maximally Symmetric Spaces
26
3
Representation of Maximally Symmetric Spaces
29
2
Maximally Symmetric Sub--spaces
31
1
Totally Geodesic Hypersurfaces
32
3
Maximally Symmetric Totally Geodesic Hypersurface
34
1
Totally Geodesic Sub-spaces
35
1
Maximally Symmetric Totally Geodesic Sub-spaces
35
1
The 2+1 BTZ Solution as Hypersurface of the 3+1 PC Metric
35
4
The Static BTZ Solution as Anti- de-Sitter Metric
37
2
Discussion of the theta formula for the Ernst potential of the rigidly rotating disk of dust
39
14
Andreas Kleinwachter
The theta formula for the Ernst potential
39
3
Calculation of the arguments
42
6
Transformation of the theta formula
48
2
Applications
50
1
Appendix
50
3
The superposition of null dust beams in General Relativity
53
10
Dietrich Kramer
Introduction
53
2
The superposition of spherically symmetric beams of null dust
55
1
The gravitational field of two counter-moving beams of light
56
4
The problem to be solved. Basic assumptions
56
1
The static solution
57
2
The stationary solution
59
1
Other solutions
60
1
Discussion
60
3
Solving equilibrium problem for the double-Kerr spacetime
63
6
Vladimir S. Manko
Eduardo Ruiz
Introduction
63
1
A short history of the problem
63
1
A new approach to the double-Kerr equilibrium problem
64
2
The Komar masses and angular momenta
66
1
Towards the analysis of the multi-black hole equilibrium states
67
2
Rotating equilibrium configurations in Einstein's theory of gravitation
69
8
Reinhard Meinel
Figures of equilibrium of rotating fluid masses
69
2
Rotating dust configurations - The Maclaurin disk
71
1
General-relativistic continuation
72
2
Black-hole limit
74
1
Discussion
74
3
Integrability of SDYM Equations for the Moyal Bracket Lie Algebra
77
14
M. Przanowski
J.F. Plebanski
S. Formanski
Introduction
77
2
Nonlocal conservation laws
79
1
Linear systems for ME
80
2
Twistor construction
82
2
The case of
84
7
Part II Alternative Theories and Scalar Fields
The FRW Universes with Barotropic Fluids in Jordan-Brans-Dicke Theory
91
10
P. Chavvet-Alducin
Introduction
91
2
Barotropic Fluids
93
2
Radiation
95
2
Vacuum
97
1
Conclusions
98
3
Higgs-Field and Gravity
101
10
Heinz Dehnen
Higgs-field gravity
101
4
Higgs-field scalar tensor theory of gravity
105
6
The road to Gravitational S-duality
111
12
H. Garcia-Compean
O. Obregon
C. Ramirez
M. Sabido
Introduction
112
1
S-Duality in Topological Gravity
113
3
S-Duality in MacDowell-Mansouri Gauge Theory of Gravity
116
3
(Anti)Self-duality of the Three-dimensional Chern-Simons Gravity
119
1
ChernSimons Gravity Dual Action in Three Dimensions
120
1
Concluding Remarks
121
2
Exact solutions in multidimensional gravity with p-branes and PPN Parameters
123
10
V. D. Ivashchuk
V. N. Melnikov
Introduction
123
1
The model
124
2
Ansatz for composite p-branes
124
1
The sigma model
125
1
Toda-type solutions from null-geodesic method
126
2
Cosmological solutions
128
1
Solutions with Ricci-flat spaces
128
1
Solutions with one curved space
128
1
Black hole solutions
129
1
Post-Newtonian approximation
130
3
Effective four-dimensional dilaton gravity from five-dimensional Chern-Simons gravity
133
8
Alfredo Macias
Alberto Garcia
Introduction
133
1
Chern-Simons action in five dimensions
134
2
Five dimensional principal fiber boundle
136
1
Effective action
137
3
Discussion
140
1
A plane-fronted wave solution in metric-affine gravity
141
14
Dirk Puetzfeld
Introduction
141
1
MAG in general
142
2
The triplet ansatz
144
1
Plane-fronted waves in GR
145
3
Plane-fronted waves in MAG
148
3
Summary
151
4
Part III Cosmology and Inflation
New solutions of Bianchi models in scalar-tensor theories
155
10
Jorge L. Cervantes-Cota
M. A. Rodriguez-Meza
Marcos Nahmad
Introduction
155
1
Equations for FRW and Bianchi models
156
2
Solutions and asymptotic behavior in BD theory
158
4
FRW solutions
159
1
Bianchi type I model
160
1
Bianchi type V model
161
1
Bianchi type IX model
161
1
Conclusions
162
3
Scalar Field Dark Matter
165
20
Tonatiuh Matos
F. Siddhartha Guzman
L. Arturo Urena-Lopez
Dario Nunez
Introduction
166
2
Cosmological Scalar Field Solutions
168
6
Radiation Dominated Era (RD)
169
2
Matter Dominated Era (MD) and Scalar Field Dominated Era
170
Scalar Power Spectrum for dark matter
171
3
Scalar dark matter and Planck scale physics
174
2
Spherical Scalar Field Fluctuations as Galactic Halos
176
5
The Galaxy Center
181
1
Conclusions
182
3
Inflation with a blue eigenvalue spectrum
185
10
Eckehard W. Mielke
Franz E. Schunck
Introduction
185
2
Spatially flat inflationary universe
187
1
Abel equation from second-order slow-roll approximation
188
2
Solutions with a blue spectrum
189
1
Complete eigenvalue spectrum
190
2
Discussion
192
3
Classical and Quantum cosmology with and without self-interacting scalar field in Bergmann-Wagoner theory
195
10
Luis O. Pimentel
Cesar Mora
Introduction
195
1
Isotropic models
196
4
Gauge N=1
197
1
Case Λ, k = 1
197
1
Case Λ, k = 0
198
1
Gauge N=1/x
198
1
Classical solutions
199
1
Classical solutions for Brans-Dicke theory
199
1
Anisotropic models
200
2
Exact solutions for Bianchi I with Λ(y) = Λ0
201
1
Solutions for Bianchi I with another potential
201
1
Exact solutions for Bianchi II with Λ(y) = Λ0
202
1
Final remarks
202
3
The Big Bang in T3 Gowdy Cosmological Models
205
8
Hernando Quevedo
Introduction
205
1
Gowdy T3 Cosmological Models
206
2
Analogies and general results
208
2
The Big Bang
210
3
The influence of scalar fields in protogalactic interactions
213
10
M. A. Rodriguez-Meza
Jaime Klapp
Jorge L. Cervantes-Cota
Heinz Dehnen
Introduction
213
2
Scalar Fields and the Newtonian Approximation
215
1
Protogalactic Cloud Models and Results
216
3
Conclusions
219
4
Adaptive Calculation of a Collapsing Molecular Cloud Core: The Jeans Condition
223
12
Leonardo D. G. Sigalotti
Jaime Klapp
Introduction
223
2
Initial Model and Computational Methods
225
3
Results
228
4
Conclusions
232
3
Revisiting the calculation of inflationary perturbations
235
12
Cesar A. Terrero-Escalante
Dominik J. Schwarz
Alberto Garcia
Introduction
235
1
The standard formulas
236
5
Amplitudes of inflationary perturbations
237
2
The spectral indices
239
2
Generalizing the Bessel approximation
241
3
Generalized power-law approximation
241
1
Generalized slow-roll approximation
242
1
The spectral indices
242
1
An alternative for more general models
243
1
Testing the expressions
244
1
Conclusions
245
2
Conformal symmetry and deflationary gas universe
247
16
Winfried Zimdahl
Alexander B. Balakin
Introduction
247
2
Fluid description
249
1
Gas dynamics
250
2
Cosmological dynamics and conformal symmetry
252
3
Phenomenological vacuum decay
255
1
Equivalent scalar field dynamics
256
1
Conclusions
257
6
Part IV Experiments and Other Topics
Staticity Theorem for Non-Rotating Black Holes with Non-Minimally Coupled Self-Interacting Scalar Fields
263
8
Eloy Ayon-Beato
Introduction
263
2
The Staticity Theorem for Non-Minimally Coupled Scalar Fields
265
4
Conclusions
269
2
Quantum nondemolition measurements and non-Newtonian gravity
271
10
A. Camacho
Introduction
271
2
Yukawa term
273
1
Quantum Measurements
274
1
Quantum nondemolition measurements
275
1
QND and non-Newtonian gravity: Propagators and probabilities
276
1
Conclusions
277
4
On Electromagnetic Thirting Problems
281
14
Markus King
Herbert Pfister
Introduction
281
1
The Static Two-Shell Model
282
3
First Order Rotation of the Shells
285
3
Results
288
7
Results in first order of the charge q
289
2
Results in second order of the charge q
291
1
Results exact in mass M and charge q
292
3
On the experimental foundation of Maxwell's equations
295
16
C. Lammerzahl
Introduction
295
1
Quantum gravity inspired modification of Maxwell's equations
296
3
Loop gravity induced corrections
297
1
String theory induced modifications
298
1
The general structure of modified dispersion relations
299
1
Tests of Maxwell's equations
299
1
Laboratory Tests
300
3
Dispersion
300
1
Charge conservation
301
1
Direct tests
301
1
Time dependence of the fine structure constant
301
1
Field of point charge
301
1
Cavendish experiments
301
1
Behaviour of atomic clocks
302
1
Tests of Special Relativity
302
1
Superposition principle
303
1
Astrophysical observations
303
4
Dispersion
305
1
High energy cosmic rays
305
1
Birefringence
306
1
Charge conservation
307
1
Magnetic fields
307
1
Tests for special Relativity
307
1
Conclusion
307
4
Lorentz force free charged fluids in general relativity: The physical interpretation
311
10
Nikolai V. Mitskievich
Introduction
311
3
LFFS in general relativity
314
3
The ansatz of zero Lorentz force in special relativistic electrodynamics
317
1
Conclusions
318
3
Index
321