Verfügbarkeit: The conformal structure of space time

The conformal structure of space time: geometry, analysis, numerics

Gespeichert in:

Bibliographische Detailangaben
Format:	Buch
Sprache:	English
Veröffentlicht:	Berlin [u.a.] Springer 2002
Schriftenreihe:	Lecture notes in physics 604
Schlagworte:	Física Conformal geometry Space and time Raum-Zeit Konforme Struktur Konferenzschrift > 2002 > Tübingen
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XIV, 372 S. graph. Darst.
ISBN:	3540442804

Internformat

MARC


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245	1	0	\|a The conformal structure of space time \|b geometry, analysis, numerics \|c J. Frauendiener ... (ed.)
246	1	3	\|a The conformal structure of space-time
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Datensatz im Suchindex

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adam_text	CONTENTS 1 CONFORMAL EINSTEIN EVOLUTION HELMUT FRIEDRICH ................................................... 1 1.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 THE CONFORMAL FIELD EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 CONFORMAL GEOMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.2 DERIVATION OF THE CONFORMAL FIELD EQUATIONS . . . . . . . . . . . 9 1.3 THE PENROSE PROPOSAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.4 ASYMPTOTIC BEHAVIOUR OF VACUUM FIELDS WITH VANISHING COSMOLOGICAL CONSTANT . . . . . . . . . . . . . . . . . . . . . . . 29 1.4.1 THE HYPERBOLOIDAL INITIAL VALUE PROBLEM. . . . . . . . . . . . . . . 30 1.4.2 ON THE EXISTENCE OF ASYMPTOTICALLY SIMPLE VACUUM SOLUTIONS . . . . . . . . . . . . 31 1.4.3 THE REGULAR FINITE CAUCHY PROBLEM. . . . . . . . . . . . . . . . . . . 33 1.4.4 TIME-LIKE INFINITY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2 SOME GLOBAL RESULTS FOR ASYMPTOTICALLY SIMPLE SPACE-TIMES GREGORY J. GALLOWAY ................................................ 51 2.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.2 THE NULL SPLITTING THEOREM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.3 PROOF OF THEOREM 2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.4 CONCLUDING REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3 BLACK HOLES PIOTR T. CHRU´ SCIEL ................................................. 61 3.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.2 EXPERIMENTAL EVIDENCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.3 CAUSALITY FOR SYMMETRIC HYPERBOLIC SYSTEMS . . . . . . . . . . . . . . . . . 65 3.3.1 DUMB HOLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.3.2 OPTICAL HOLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 3.3.3 TRAPPED SURFACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 3.4 STANDARD BLACK HOLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.4.1 SCRI REGULARITY CONDITIONS, AND THE AREA THEOREM . . . . . . 75 3.5 HORIZONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.6 APPARENT HORIZONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 X CONTENTS 3.7 CLASSIFICATION OF STATIONARY SOLUTIONS (NO HAIR THEOREMS) . . . . 80 3.8 BLACK HOLES WITHOUT SCRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.8.1 NAIVE BLACK HOLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.8.2 QUASI-LOCAL BLACK HOLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.8.3 FINDING HORIZONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4 CONFORMAL GEOMETRY, DIFFERENTIAL EQUATIONS AND ASSOCIATED TRANSFORMATIONS SIMONETTA FRITTELLI, NIKY KAMRAN, EZRA T. NEWMAN .................... 103 4.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 4.2 EXAMPLE OF CONTACT-ENVELOPE TRANSFORMATION . . . . . . . . . . . . . . . . . 105 4.3 GENERALIZATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 4.3.1 THREE-DIMENSIONAL CONFORMAL LORENTZIAN GEOMETRIES . . . . 109 4.3.2 FOUR-DIMENSIONAL CONFORMAL LORENTZIAN GEOMETRIES . . . . . 110 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 5 TWISTOR GEOMETRY OF CONFORMAL INFINITY ROGER PENROSE ..................................................... 113 5.1 NON-LINEAR GRAVITONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.2 THE REASONABLENESS OF I + . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 5.3 THE CONSTRUCTION OF PROJECTIVE TWISTOR SPACE P T FROM I + . . . . . 115 5.4 THE CONSTRUCTION OF THE FULL TWISTOR SPACE T FROM I + . . . . . . . . 117 5.5 THE LOCAL STRUCTURE OF TWISTOR SPACE P T . . . . . . . . . . . . . . . . . . . . 118 5.6 PRESENT STATUS OF THE ROLE OF T IN ENCODING RICCI-FLATNESS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 6 ISOTROPIC COSMOLOGICAL SINGULARITIES K. PAUL TOD ....................................................... 123 6.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6.2 FORMALISM AND EXTENSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 6.3 REVIEW OF POLYTROPIC PERFECT FLUID CASE . . . . . . . . . . . . . . . . . . . . . . 128 6.4 FURTHER MATTER MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 6.4.1 MASSIVE EINSTEIN-VLASOV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 6.4.2 SCALAR FIELDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 6.4.3 EINSTEIN-YANG-MILLS-VLASOV . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 6.4.4 EINSTEIN-BOLTZMANN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 6.5 CONCLUSION AND FUTURE POSSIBILITIES . . . . . . . . . . . . . . . . . . . . . . . . . . 133 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 7 POLYHOMOGENEOUS EXPANSIONS CLOSE TO NULL AND SPATIAL INFINITY JUAN ANTONIO VALIENTE KROON ........................................ 135 7.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 7.2 MINKOWSKI SPACE-TIME CLOSE TO NULL AND SPATIAL INFINITY . . . . . . . 136 7.3 LINEARISED GRAVITY IN THE F-GAUGE . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 CONTENTS XI 7.3.1 INITIAL DATA FOR LINEARISED GRAVITY . . . . . . . . . . . . . . . . . . . . 140 7.4 A REGULARITY CONDITION AT SPATIAL INFINITY . . . . . . . . . . . . . . . . . . . . 142 7.5 POLYHOMOGENEOUS EXPANSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 7.5.1 A SUBSTRACTION ARGUMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 7.5.2 AN INVESTIGATION OF EXPANSIONS CLOSE TO NULL INFINITY . . . . 147 7.5.3 CONCLUDING REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 8 ASYMPTOTICALLY FLAT AND REGULAR CAUCHY DATA SERGIO DAIN ....................................................... 161 8.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 8.2 SOLUTION OF THE HAMILTONIAN CONSTRAINT WITH LOGARITHMIC TERMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 8.3 EXPLICIT SOLUTIONS OF THE MOMENTUM CONSTRAINT . . . . . . . . . . . . . . . 173 8.3.1 THE MOMENTUM CONSTRAINT ON EUCLIDEAN SPACE . . . . . . . . . 173 8.3.2 AXIALLY SYMMETRIC INITIAL DATA . . . . . . . . . . . . . . . . . . . . . . . 176 8.4 MAIN IDEAS IN THE PROOF OF THEOREM 8.1 . . . . . . . . . . . . . . . . . . . . . . 178 8.5 FINAL COMMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 9 CONSTRUCTION OF HYPERBOLOIDAL INITIAL DATA LARS ANDERSSON .................................................... 183 9.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 9.2 PRELIMINARIES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 9.3 CONFORMAL RESCALINGS OF MINKOWSKI SPACE . . . . . . . . . . . . . . . . . . . . 185 9.4 CONFORMAL CONSTRAINT EQUATIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 9.4.1 CONSTANT MEAN CURVATURE HYPERSURFACES. . . . . . . . . . . . . . . 188 9.4.2 DEGENERATE ELLIPTIC EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . 189 9.4.3 REGULARITY OF SOLUTIONS TO THE CONFORMAL CONSTRAINT EQUATIONS . . . . . . . . . . . . . . . . 190 9.5 THE INITIAL VALUE PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 9.5.1 GAUGE CONDITION AT M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 9.5.2 EVOLUTION AT M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 9.6 DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 10 EXPLORING THE CONFORMAL CONSTRAINT EQUATIONS ADRIAN BUTSCHER ................................................... 195 10.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 10.2 THE CONFORMAL CONSTRAINT EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . 197 10.2.1 DERIVING THE EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 10.2.2 REDUCTION TO THE EXTENDED CONSTRAINT EQUATIONS . . . . . . . 201 10.2.3 PROPERTIES OF THE EXTENDED CONSTRAINT EQUATIONS . . . . . . . 202 10.3 ASYMPTOTICALLY FLAT SOLUTIONS OF THE EXTENDED CONSTRAINT EQUATIONS IN THE TIME SYMMETRIC CASE. . . . . . . . . . . . . 206 10.3.1 STATEMENT OF THE MAIN THEOREM . . . . . . . . . . . . . . . . . . . . . . 206 XII CONTENTS 10.3.2 FORMULATING AN ELLIPTIC PROBLEM . . . . . . . . . . . . . . . . . . . . . . 208 10.3.3 CHOOSING THE BANACH SPACES . . . . . . . . . . . . . . . . . . . . . . . . . 209 10.3.4 FIRST ATTEMPT TO SOLVE THE ASSOCIATED SYSTEM . . . . . . . . . 212 10.3.5 REESTABLISHING SURJECTIVITY AND SOLVING THE ASSOCIATED SYSTEM . . . . . . . . . . . . . . . . . . . . 215 10.3.6 SATISFYING THE HARMONIC COORDINATE CONDITION. . . . . . . . . . 217 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 11 CRITERIA FOR (IN)FINITE EXTENT OF STATIC PERFECT FLUIDS WALTER SIMON ..................................................... 223 11.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 11.2 THE MAIN THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 11.3 THE VIRIAL THEOREM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 11.4 PROOF OF THE MAIN THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 11.5 DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 12 PROBLEMS AND SUCCESSES IN THE NUMERICAL APPROACH TO THE CONFORMAL FIELD EQUATIONS SASCHA HUSA ...................................................... 239 12.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 12.2 ALGORITHMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 12.2.1 PROBLEM OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 12.2.2 CONSTRUCTION OF EXTENDED HYPERBOLOIDAL INITIAL DATA . . 243 12.2.3 BLACK HOLE INITIAL DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 12.2.4 NUMERICAL SETUP FOR EVOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . 247 12.2.5 PHYSICS EXTRACTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 12.3 RESULTS FOR WEAK DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 12.4 COMPUTATIONAL ASPECTS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 12.5 DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 13 SOME ASPECTS OF THE NUMERICAL TREATMENT OF THE CONFORMAL FIELD EQUATIONS J¨ ORG FRAUENDIENER .................................................. 261 13.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 13.2 THE ANDERSSON-CHRU´ SCIEL-FRIEDRICH PROCEDURE . . . . . . . . . . . . . . . . . 263 13.3 THE LICHN´ EROWICZYAMABEEQUATION . . . . . . . . . . . . . . . . . . . . . . . . . 266 13.4 CONSTRUCTING INITIAL DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 13.5 CONCLUSION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 14 DATA FOR THE NUMERICAL CALCULATION OF THE KRUSKAL SPACE-TIME BERND G. SCHMIDT .................................................. 283 14.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 14.2 CONFORMAL EXTENSION OF THE KRUSKAL SPACE-TIME. . . . . . . . . . . . . . . 284 CONTENTS XIII 14.3 A SPACE-LIKE HYPERSURFACE INTERSECTING I + L AND I + R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 14.4 A FOLIATION INTERSECTING BOTH I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 14.5 NUMERICAL CALCULATION OF THE KRUSKAL SPACE-TIME . . . . . . . . . . . . . 293 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 15 NUMERICS OF THE CHARACTERISTIC FORMULATION IN BONDI VARIABLES. WHERE WE ARE AND WHAT LIES AHEAD LUIS LEHNER ....................................................... 297 15.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 15.2 CHARACTERISTIC FORMULATION OF GR IN BONDI VARIABLES . . . . . . . . . . . 298 15.2.1 INITIAL BOUNDARY VALUE PROBLEM . . . . . . . . . . . . . . . . . . . . . . 299 15.2.2 NEWS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 15.2.3 INERTIAL COORDINATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 15.3 NUMERICAL DETAILS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 15.4 APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 15.4.1 BLACK HOLE-STAR BINARIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 15.4.2 BINARY BLACK HOLE PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . . . 308 15.5 FINAL COMMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 16 NUMERICAL EXPERIMENTS AT NULL INFINITY ROBERT A. BARTNIK, ANDREW H. NORTON ................................ 313 16.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 16.2 NQS METRICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 16.3 NQS FORMAL ASYMPTOTICS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 16.4 GENERICITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 16.5 THE NQS CODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 16.6 NUMERICAL RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 17 LOCAL CHARACTERISTIC ALGORITHMS FOR RELATIVISTIC HYDRODYNAMICS JOS´ E A. FONT ...................................................... 327 17.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 17.2 RELATIVISTIC HYDRODYNAMIC EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . 329 17.3 HIGH-RESOLUTION NUMERICAL SCHEMES . . . . . . . . . . . . . . . . . . . . . . . . . 332 17.4 APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 17.4.1 SHOCK TUBE TEST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 17.4.2 GRAVITATIONAL COLLAPSE OF SUPERMASSIVE STARS . . . . . . . . . . . 338 17.4.3 NULL CONE EVOLUTION OF RELATIVISTIC STARS. . . . . . . . . . . . . . . 340 17.5 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344 XIV CONTENTS 18 SIMULATIONS OF GENERIC SINGULARITIES IN HARMONIC COORDINATES DAVID GARFINKLE .................................................... 349 18.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 18.2 EQUATIONS AND NUMERICAL METHODS. . . . . . . . . . . . . . . . . . . . . . . . . . . 351 18.3 RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 18.4 DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 19 SOME MATHEMATICAL AND NUMERICAL QUESTIONS CONNECTED WITH FIRST AND SECOND ORDER TIME-DEPENDENT SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS HEINZ-O. KREISS, OMAR E. ORTIZ ..................................... 359 19.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 19.2 WELL POSED PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 19.2.1 FIRST ORDER SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 19.2.2 SECOND ORDER SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 19.3 SECOND ORDER INITIAL VALUE FORMULATIONS FOR GENERAL RELATIVITY . . 364 19.4 DIFFERENCE APPROXIMATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366 19.5 CONSTRAINTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370
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spelling	The conformal structure of space time geometry, analysis, numerics J. Frauendiener ... (ed.) The conformal structure of space-time Berlin [u.a.] Springer 2002 XIV, 372 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics 604 Physics and astronomy online library Física larpcal Conformal geometry Space and time Raum-Zeit (DE-588)4302626-6 gnd rswk-swf Konforme Struktur (DE-588)4500911-9 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2002 Tübingen gnd-content Raum-Zeit (DE-588)4302626-6 s Konforme Struktur (DE-588)4500911-9 s DE-604 Frauendiener, Jörg Sonstige oth Lecture notes in physics 604 (DE-604)BV000003166 604 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010022082&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	The conformal structure of space time geometry, analysis, numerics Lecture notes in physics Física larpcal Conformal geometry Space and time Raum-Zeit (DE-588)4302626-6 gnd Konforme Struktur (DE-588)4500911-9 gnd
subject_GND	(DE-588)4302626-6 (DE-588)4500911-9 (DE-588)1071861417
title	The conformal structure of space time geometry, analysis, numerics
title_alt	The conformal structure of space-time
title_auth	The conformal structure of space time geometry, analysis, numerics
title_exact_search	The conformal structure of space time geometry, analysis, numerics
title_full	The conformal structure of space time geometry, analysis, numerics J. Frauendiener ... (ed.)
title_fullStr	The conformal structure of space time geometry, analysis, numerics J. Frauendiener ... (ed.)
title_full_unstemmed	The conformal structure of space time geometry, analysis, numerics J. Frauendiener ... (ed.)
title_short	The conformal structure of space time
title_sort	the conformal structure of space time geometry analysis numerics
title_sub	geometry, analysis, numerics
topic	Física larpcal Conformal geometry Space and time Raum-Zeit (DE-588)4302626-6 gnd Konforme Struktur (DE-588)4500911-9 gnd
topic_facet	Física Conformal geometry Space and time Raum-Zeit Konforme Struktur Konferenzschrift 2002 Tübingen
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