3+1 formalism and bases of numerical relativity - LUTh ...

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214 BIBLIOGRAPHY [226] M. Shibata : Fully general relativistic simulation of coalescing binary neutron stars: Preparatory tests, Phys. Rev. D 60, 104052 (1999). [227] M. Shibata : Axisymmetric general relativistic hydrodynamics: Long-term evolution of neutron stars and stellar collapse to neutron stars and black holes, Phys. Rev. D 67, 024033 (2003). [228] M. Shibata : Collapse of Rotating Supramassive Neutron Stars to Black Holes: Fully General Relativistic Simulations, Astrophys. J. 595, 992 (2003). [229] M. Shibata, T.W. Baumgarte, and S.L. Shapiro : Stability and collapse of rapidly rotating, supramassive neutron stars: 3D simulations in general relativity, Phys. Rev. D 61, 044012 (2000). [230] M. Shibata, T.W. Baumgarte, and S.L. Shapiro : The Bar-Mode Instability in Differentially Rotating Neutron Stars: Simulations in Full General Relativity, Astrophys. J. 542, 453 (2000). [231] M. Shibata, Y.T. Liu, S.L. Shapiro, and B.C. Stephens : Magnetorotational collapse of massive stellar cores to neutron stars: Simulations in full general relativity, Phys. Rev. D 74, 104026 (2006). [232] M. Shibata and T. Nakamura : Conformal Time Slicing Condition in Three Dimensional Numerical Relativity, Prog. Theor. Phys. 88, 317 (1992). [233] M. Shibata and T. Nakamura : Evolution of three-dimensional gravitational waves: Harmonic slicing case, Phys. Rev. D 52, 5428 (1995). [234] M. Shibata and Y. Sekiguchi : Three-dimensional simulations of stellar core collapse in full general relativity: Nonaxisymmetric dynamical instabilities, Phys. Rev. D 71, 024014 (2005). [235] M. Shibata and Y. Sekiguchi : Magnetohydrodynamics in full general relativity: Formulation and tests, Phys. Rev. D 72, 044014 (2005). [236] M. Shibata and K. Taniguchi : Merger of binary neutron stars to a black hole: Disk mass, short gamma-ray bursts, and quasinormal mode ringing, Phys. Rev. D 73, 064027 (2006). [237] M. Shibata, K. Taniguchi, and K. Uryu : Merger of binary neutron stars of unequal mass in full general relativity, Phys. Rev. D 68, 084020 (2003). [238] M. Shibata, K. Taniguchi, and K. Uryu : Merger of binary neutron stars with realistic equations of state in full general relativity, Phys. Rev. D 71, 084021 (2005). [239] M. Shibata and K. Uryu : Simulation of merging binary neutron stars in full general relativity: Γ = 2 case, Phys. Rev. D 61, 064001 (2000). [240] M. Shibata and K. Uryu : Gravitational Waves from the Merger of Binary Neutron Stars in a Fully General Relativistic Simulation, Prog. Theor. Phys. 107, 265 (2002).
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arXiv:gr-qc/0703035v1 6 Mar 2007 3+
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4 CONTENTS 3.3.6 Evolution of the o
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6 CONTENTS 8 The initial data probl
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8 CONTENTS
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10 CONTENTS
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12 Introduction 3D (no symmetry at
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14 Introduction
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16 Geometry of hypersurfaces in two
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18 Geometry of hypersurfaces 2.2.3
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20 Geometry of hypersurfaces Figure
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22 Geometry of hypersurfaces •
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24 Geometry of hypersurfaces The ei
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26 Geometry of hypersurfaces Figure
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28 Geometry of hypersurfaces The no
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30 Geometry of hypersurfaces Since
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32 Geometry of hypersurfaces 2.4.3
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34 Geometry of hypersurfaces 2.5 Ga
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36 Geometry of hypersurfaces Exampl
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38 Geometry of hypersurfaces
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40 Geometry of foliations Figure 3.
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42 Geometry of foliations 3.3.2 Nor
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44 Geometry of foliations means Eq.
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46 Geometry of foliations Remark :
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48 Geometry of foliations Note that
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50 Geometry of foliations
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52 3+1 decomposition of Einstein eq
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72 3+1 equations for matter and ele
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84 Conformal decomposition equivale
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86 Conformal decomposition As an ex
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88 Conformal decomposition 6.2.4 Co
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90 Conformal decomposition 6.3.1 Ge
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92 Conformal decomposition where K
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94 Conformal decomposition to write
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96 Conformal decomposition hence Lm
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98 Conformal decomposition 6.5.2 Ha
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100 Conformal decomposition discuss
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102 Conformal decomposition Remark
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104 Asymptotic flatness and global
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126 The initial data problem Notice
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128 The initial data problem where
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130 The initial data problem 8.2.3
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132 The initial data problem where
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134 The initial data problem Figure
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136 The initial data problem Figure
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138 The initial data problem In par
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140 The initial data problem Accord
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142 The initial data problem Remark
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144 The initial data problem Remark
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146 The initial data problem 8.4.1
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148 The initial data problem Since
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150 The initial data problem • fo
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152 Choice of foliation and spatial
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Page 190 and 191: 190 Lie derivative Figure A.1: Geom
Page 192 and 193: 192 Lie derivative
Page 194 and 195: 194 Conformal Killing operator and
Page 200 and 201: 200 BIBLIOGRAPHY [13] A. Anderson a
Page 202 and 203: 202 BIBLIOGRAPHY [43] T.W. Baumgart
Page 204 and 205: 204 BIBLIOGRAPHY [75] M. Campanelli
Page 206 and 207: 206 BIBLIOGRAPHY [105] G. Darmois :
Page 208 and 209: 208 BIBLIOGRAPHY [135] H. Friedrich
Page 210 and 211: 210 BIBLIOGRAPHY [163] J. Isenberg
Page 212 and 213: 212 BIBLIOGRAPHY [195] S. Nissanke
Page 216 and 217: 216 BIBLIOGRAPHY [255] K. Taniguchi
Page 218 and 219: Index 1+log slicing, 161 3+1 formal
Page 220: 220 INDEX Ricci identity, 18 Ricci
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