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Theta formula for the Ernst potential of the rigidly rotating disk of dust with and The value of (6) in the upper sheet of the surface is defined by for The two normalized Abelian differentials of the first kind are defined by The values of and have to be determined by integration over an Abelian differential of the third kind with the requirement: 41
42 EXACT SOLUTIONS AND SCALAR FIELDS IN GRAVITY The remaining quantities are defined to be The goal is now to calculate all the arguments once and for all so that for applications it is not necessary to consider the Riemann surface and Abelian differentials. This is done in the next section. Using these results, the theta formula will then be recast. The resulting formulae can be very easily numerically handled. This is summarized in the last section. 2. CALCULATION OF THE ARGUMENTS Using the notation the cuts are than denoted by with: Now the behavior of the “fundamental root” (6) is carefully investigated. Therefore the “elementary root” for the complex quantity jumping at the cut is introduced as: where the choice is made. The fundamental root (6) can be built up from (16) using the definitions (12)–(14) by: The radicand of (16) is given by:
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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
Page 16 and 17: PREFACE This book is dedicated to h
Page 18 and 19: CONTRIBUTING AUTHORS Eloy Ayón-Bea
Page 20 and 21: Contributing Authors xix Jaime Klap
Page 22 and 23: Contributing Authors xxi A.P. 70-54
Page 24 and 25: Contributing Authors xxiii L. Artur
Page 26 and 27: I EXACT SOLUTIONS
Page 28 and 29: SELF-GRAVITATING STATIONARY AXI- SY
Page 30 and 31: Self-gravitating stationary axisymm
Page 38 and 39: REFERENCES 13 be shown that the ana
Page 40 and 41: NEW DIRECTIONS FOR THE NEW MILLENNI
Page 42 and 43: New Directions for the New Millenni
Page 44 and 45: New Directions for the New Millenni
Page 46 and 47: REFERENCES 21 Acknowledgments The r
Page 48 and 49: ON MAXIMALLY SYMMETRIC AND TOTALLY
Page 50 and 51: On maximally symmetric and totally
Page 64 and 65: DISCUSSION OF THE THETA FORMULA FOR
Page 68 and 69: Theta formula for the Ernst potenti
Page 76 and 77: REFERENCES 51 Rosenhain’s theta f
Page 78 and 79: THE SUPERPOSITION OF NULL DUST BEAM
Page 80 and 81: The superposition of null dustbeams
Page 86 and 87: REFERENCES 61 geodesic with respect
Page 88 and 89: SOLVING EQUILIBRIUM PROBLEM FOR THE
Page 90 and 91: Solving equilibrium problem for the
Page 92 and 93: REFERENCES 67 where the subindices
Page 94 and 95: ROTATING EQUILIBRIUM CONFIGURATIONS
Page 96 and 97: Rotating equilibrium configurations
Page 98 and 99: Rotating equilibrium configurations
Page 100 and 101: REFERENCES 75 5. DISCUSSION The ana
Page 102 and 103: INTEGRABILITY OF SDYM EQUATIONS FOR
Page 104 and 105: Integrability of SDYM Equations for
Page 112 and 113: REFERENCES 87 [18] [19] [20] [21] [
Page 114 and 115: II ALTERNATIVE THEORIES AND SCALAR
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THE FRW UNIVERSES WITH BAROTROPIC F
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The FRW Universes with Barotropic F
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REFERENCES 99 (1979) 515; H. Dehnen
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HIGGS-FIELD AND GRAVITY Heinz Dehne
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Higgs-Field and Gravity 103 is defi
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Higgs-Field and Gravity 105 Consequ
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Higgs-Field and Gravity 107 From th
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REFERENCES 109 Evidently by inserti
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THE ROAD TO GRAVITATIONAL S-DUALITY
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The road to Gravitational S-duality
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REFERENCES 121 The partition functi
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EXACT SOLUTIONS IN MULTIDIMENSIONAL
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Exact solutions in multidimensional
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REFERENCES 131 For possible physica
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EFFECTIVE FOUR-DIMENSIONAL DILATON
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Dilaton gravity from Chern-Simons g
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A PLANE-FRONTED WAVE SOLUTION IN ME
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A plane-fronted wave solution in me
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REFERENCES 6. SUMMARY 151 We invest
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III COSMOLOGY AND INFLATION
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NEW SOLUTIONS OF BIANCHI MODELS IN
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New solutions of Bianchi models in
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REFERENCES 163 Further solutions of
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SCALAR FIELD DARK MATTER Tonatiuh M
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Scalar field dark matter 167 tional
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Scalar field dark matter 169 being
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Scalar field dark matter 171 of dar
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Scalar field dark matter 173 growin
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Scalar field dark matter 175 This s
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Scalar field dark matter 177 rotati
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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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