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Prof. Dietrich Kramer: Brief Biography Dietrich Kramer was born in Weida, in a small and nice village in Thuringen, Germany. He studied Physics at the Friedrich Schiller University of Jena and got his Diploma in 1962, at the age of 22. In 1966 he finished his Ph.D. at the same University, working in problems of bispinors in curved spaces. Since those years curved space–times and General Relativity have been his passions. In 1969 he published together with Gernot Neugabauer a paper in Annalen der Physik (Leipzig), where the definition of the Ernst potentials is given. They discovered and studied the potentials independently at the same time as Fred Ernst did. These potentials are maybe one of the most important results of the last times in General Relativity The Annalen der Physik Journal was not very well known at the time of the cold war, for this reason only few people were able to read the work of Kramer and Neugebauer. In this work, they proposed a method to generate exact solutions of the axially symmetric exterior fields of the Einstein field equations, by using subgroups and subspaces of the whole isometry group of these space–times. Many other people all over the world developed later this method further. A lot of the well–known exact solutions of the Einstein field equations can be generated using this elegant, powerful and simple method. Dietrich Kramer got his Habilitation in 1970 with the thesis: Invariantztransformationen strenger Vakumlösungen in der allgemeine Relativitätstheorie. In 1980, together with Hans Stephani, Malcolm Mac- Callum and Eduard Held, he wrote the historical monograph: Exact Solutions to the Einstein Field Equations, one of the most important books of General Relativity, indispensable textbook for people working on Differential Geometry, curved spaces or partial differential equations connected with the Einstein equations. In 1981, together with Gernot Neugabauer, Dietrich Kramer was awarded with the price of the General Relativity Foundation. Since 1992 he is Professor for Theoretical Physics in Gravitational Theory at Friedrich Schiller University of Jena. Among other positions, Dietrich Kramer has been Dean of the Institute for Theoretical Physics of the same University. Prof. Kramer has delivered invited talks at many of the most important Universities and international conferences of the world. He maintains good scientific relationships with other groups of relativity, in particular with groups in Madrid and in Mexico at Cinvestav. 327
328 EXACT SOLUTIONS AND SCALAR FIELDS IN GRAVITY We learned a lot from Professor Dietrich Kramer, such as General Relativity, exact solutions, etc. However, his best lecture has been his example as kind and modest person, human being, and physicist. We are honoured for celebrating here his birthday with this conference. TONATIUH MATOS
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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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REFERENCES 87 [18] [19] [20] [21] [
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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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Quantum nondemolition measurements
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Page 336 and 337: LORENTZ FORCE FREE CHARGED FLUIDS I
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Page 346 and 347: Index Axisymmetries and configurati
Page 348 and 349: INDEX 323 Theorem (cont.) staticity
Page 350 and 351: Prof. Heinz Dehnen: Brief Biography
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