did-you-know? rent-now

Amazon no longer offers textbook rentals. We do!

did-you-know? rent-now

Amazon no longer offers textbook rentals. We do!

We're the #1 textbook rental company. Let us show you why.

9780306466182

Exact Solutions and Scalar Fields in Gravity

by ; ;
  • ISBN13:

    9780306466182

  • ISBN10:

    030646618X

  • Format: Hardcover
  • Copyright: 2001-08-01
  • Publisher: Plenum Pub Corp
  • Purchase Benefits
  • Free Shipping Icon Free Shipping On Orders Over $35!
    Your order must be $35 or more to qualify for free economy shipping. Bulk sales, PO's, Marketplace items, eBooks and apparel do not qualify for this offer.
  • eCampus.com Logo Get Rewarded for Ordering Your Textbooks! Enroll Now
  • Write a Review Icon Write a Review
List Price: $179.99 Save up to $146.58
  • Digital
    $72.39
    Add to Cart

    DURATION
    PRICE

Supplemental Materials

What is included with this book?

Summary

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

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

Supplemental Materials

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

Rewards Program