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REFERENCES 131 For possible physical applications, one should calculate and using where From (47)–(51) we deduce [11, 13]: Parameter depends upon ratios of physical parameters: and does not depend upon the quasi–Cartan matrix and, hence, upon intersections of The parameter depends upon ratios where are functions of GM, and The calculation of needs an exact solution for radial functions Relations (53) and (54) coincide with those obtained in [7] for block–orthogonal case, when charges are coinciding inside blocks. For most interesting solutions with and (53) implies Acknowledgments This work was supported in part by DFG grant 436 RUS 113/236/O(R), by RFBR, grant 98–02–16414, Project SEE and CONACYT, Mexico. VNM is grateful to Depto. de Fisica, CINVESTAV for their hospitality. References [1] D. Kramer, Acta Physica Polonica 2 (1969) 807. [2] G. Neugebauer and D. Kramer, Ann. der Physik (Leipzig) 24 (1969) 62. [3] V.N.Melnikov, in: Cosmology and Gravitation, ed. M.Novello, (Editions Frontieres, Singapore, 1994) pp.147. [4] V.N.Melnikov, in: Cosmology and Gravitation II. (Editions Frontieres, Singapore, 1996) pp.465. [5] V.D.Ivashchuk and V.N.Melnikov, in: Lecture Notes in Physics, v.537. Eds. S.Cotsakis and G.Gibbons, (Springer, Berlin, 2000) pp.214.
132 EXACT SOLUTIONS AND SCALAR FIELDS IN GRAVITY [6] V.D. Ivashchuk and V.N. Melnikov, Class. Quantum Grav. 14 (1997) 3001. [7] V.D.Ivashchuk and V.N.Melnikov, J. Math. Phys., 40 (1999) 6558. [8] V.R. Gavrilov and V.N. Melnikov, TMP, 123 (2000) 374. [9] V.D.Ivashchuk and S.W. Kim, J. Math. Phys. 41 (2000) 444. [10] V.D.Ivashchuk and V.N.Melnikov, Grav. and Cosm., 5 (1999) 313. [11] V.D.Ivashchuk and V.N.Melnikov, Grav. and Cosm., 6 (2000) 27. [12] V.D.Ivashchuk and V.N.Melnikov, Class. Quantum Grav. 17 (2000) 2073. [13] V.D. Ivashchuk, V.S. Manko and V.N. Melnikov, Grav, and Cosm. 6 (2000) 23.
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EXACT SOLUTIONS AND SCALAR FIELDS I
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To the 65th birthday of Heinz Dehne
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CONTENTS Preface Contributing Autho
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Contents ix 5 The case of 84 Part I
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Contents xi Luis O. Pimentel, Cesar
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Contents xiii 2.2 String theory ind
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PREFACE This book is dedicated to h
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CONTRIBUTING AUTHORS Eloy Ayón-Bea
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Contributing Authors xix Jaime Klap
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Contributing Authors xxi A.P. 70-54
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Contributing Authors xxiii L. Artur
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I EXACT SOLUTIONS
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SELF-GRAVITATING STATIONARY AXI- SY
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Self-gravitating stationary axisymm
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REFERENCES 13 be shown that the ana
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NEW DIRECTIONS FOR THE NEW MILLENNI
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New Directions for the New Millenni
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New Directions for the New Millenni
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REFERENCES 21 Acknowledgments The r
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ON MAXIMALLY SYMMETRIC AND TOTALLY
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On maximally symmetric and totally
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DISCUSSION OF THE THETA FORMULA FOR
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Theta formula for the Ernst potenti
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REFERENCES 51 Rosenhain’s theta f
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THE SUPERPOSITION OF NULL DUST BEAM
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The superposition of null dustbeams
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REFERENCES 61 geodesic with respect
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SOLVING EQUILIBRIUM PROBLEM FOR THE
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Solving equilibrium problem for the
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REFERENCES 67 where the subindices
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ROTATING EQUILIBRIUM CONFIGURATIONS
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Rotating equilibrium configurations
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Rotating equilibrium configurations
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REFERENCES 75 5. DISCUSSION The ana
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INTEGRABILITY OF SDYM EQUATIONS FOR
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Integrability of SDYM Equations for
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Page 112 and 113: REFERENCES 87 [18] [19] [20] [21] [
Page 114 and 115: II ALTERNATIVE THEORIES AND SCALAR
Page 116 and 117: THE FRW UNIVERSES WITH BAROTROPIC F
Page 118 and 119: The FRW Universes with Barotropic F
Page 124 and 125: REFERENCES 99 (1979) 515; H. Dehnen
Page 126 and 127: HIGGS-FIELD AND GRAVITY Heinz Dehne
Page 128 and 129: Higgs-Field and Gravity 103 is defi
Page 130 and 131: Higgs-Field and Gravity 105 Consequ
Page 132 and 133: Higgs-Field and Gravity 107 From th
Page 134 and 135: REFERENCES 109 Evidently by inserti
Page 136 and 137: THE ROAD TO GRAVITATIONAL S-DUALITY
Page 138 and 139: The road to Gravitational S-duality
Page 146 and 147: REFERENCES 121 The partition functi
Page 148 and 149: EXACT SOLUTIONS IN MULTIDIMENSIONAL
Page 150 and 151: Exact solutions in multidimensional
Page 158 and 159: EFFECTIVE FOUR-DIMENSIONAL DILATON
Page 160 and 161: Dilaton gravity from Chern-Simons g
Page 166 and 167: A PLANE-FRONTED WAVE SOLUTION IN ME
Page 168 and 169: A plane-fronted wave solution in me
Page 176 and 177: REFERENCES 6. SUMMARY 151 We invest
Page 178 and 179: III COSMOLOGY AND INFLATION
Page 180 and 181: NEW SOLUTIONS OF BIANCHI MODELS IN
Page 182 and 183: New solutions of Bianchi models in
Page 188 and 189: REFERENCES 163 Further solutions of
Page 190 and 191: SCALAR FIELD DARK MATTER Tonatiuh M
Page 192 and 193: Scalar field dark matter 167 tional
Page 194 and 195: Scalar field dark matter 169 being
Page 196 and 197: Scalar field dark matter 171 of dar
Page 198 and 199: Scalar field dark matter 173 growin
Page 200 and 201: Scalar field dark matter 175 This s
Page 202 and 203: Scalar field dark matter 177 rotati
Page 204 and 205: Scalar field dark matter 179 where
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Scalar field dark matter 181 while
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REFERENCES 183 The hypothesis of th
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INFLATION WITH A BLUE EIGENVALUE SP
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Inflation with a blue eigenvalue sp
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REFERENCES 193 problem” for nonli
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CLASSICAL AND QUANTUM COSMOLOGY WIT
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Quantum cosmology with self-interac
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REFERENCES 203 [13] has considered
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THE BIG BANG IN GOWDY COSMOLOGICAL
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The Big Bang in Gowdy Cosmological
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THE INFLUENCE OF SCALAR FIELDS IN P
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The influence of scalar fields in p
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The influence of scalar fields in p
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REFERENCES 221 [3] by R.C. Kennicut
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ADAPTIVE CALCULATION OF A COLLAPSIN
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Adaptive Calculation of a Collapsin
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REFERENCES 233 [5] [6] [7] [8] [9]
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REVISITING THE CALCULATION OF INFLA
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Revisiting the calculation of infla
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CONFORMAL SYMMETRY AND DEFLATIONARY
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Conformal symmetry and deflationary
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REFERENCES 259 [16] R. Maartens, D.
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IV EXPERIMENTS AND OTHER TOPICS
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STATICITY THEOREM FOR NON-ROTATING
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Staticity Theorem for Non-Rotating
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Staticity Theorem for Non-Rotating
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REFERENCES 269 The boundary is cons
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QUANTUM NONDEMOLITION MEASUREMENTS
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Quantum nondemolition measurements
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REFERENCES 279 [11] M. Kasevich and
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ON ELECTROMAGNETIC THIRRING PROBLEM
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On Electromagnetic Thirring Problem
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REFERENCES 293 [8] [9] D. Brill and
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ON THE EXPERIMENTAL FOUNDATION OF M
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On the experimental foundation of M
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REFERENCES 309 [12] [13] [14] [15]
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LORENTZ FORCE FREE CHARGED FLUIDS I
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Lorentz force free charged fluids i
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REFERENCES 319 force can be foresee
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Index Axisymmetries and configurati
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INDEX 323 Theorem (cont.) staticity
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Prof. Heinz Dehnen: Brief Biography
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Prof. Dietrich Kramer: Brief Biogra
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