Exact Solutions and Scalar Fields in Gravity: Recent Developments

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Alfredo Macías, Jorge L. Cervantes-Cota, Claus Lämmerzahl
Springer Science & Business Media, Aug 31, 2001 - Mathematics - 328 pages
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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.
 

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Contents

Differential rota
3
Discussion of the theta formula for the Ernst potential of the rigidly rotating
6
New Directions for the New Millennium
15
On maximally symmetric and totally geodesic spaces
23
Andreas Kleinwächter
39
The superposition of null dust beams in General Relativity
53
Solving equilibrium problem for the doubleKerr spacetime
63
Rotating equilibrium configurations in Einsteins theory of gravitation
69
Inflation with a blue eigenvalue spectrum
185
Luis O Pimentel Cesar Mora
196
56
212
Condition Leonardo Di G Sigalotti Jaime Klapp
223
4
228
Classical and Quantum cosmology with and without selfinteracting scalar
248
Conclusions Part IV Experiments and Other Topics
263
6
277

Integrability of SDYM Equations for the Moyal Bracket Lie Algebra
77
The FRW Universes with Barotropic Fluids in JordanBransDicke Theory P ChauvetAlducin
91
48
149
New solutions of Bianchi models in scalartensor theories
155
Scalar Field Dark Matter
165
50
183
57
279
Alfredo Macias Alberto Garcia
311
Index
321
60
322
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