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

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216 BIBLIOGRAPHY [255] K. Taniguchi and E. Gourgoulhon : Various features of quasiequilibrium sequences of binary neutron stars in general relativity, Phys. Rev. D 68, 124025 (2003). [256] S.A. Teukolsky : Linearized quadrupole waves in general relativity and the motion of test particles, Phys. Rev. D 26, 745 (1982). [257] S.A Teukolsky : Irrotational binary neutron stars in quasi-equilibrium in general relativity, Astrophys. J. 504, 442 (1998). [258] K.S. Thorne and D. Macdonald : Electrodynamics in curved spacetime: 3+1 formulation, Mon. Not. R. Astron. Soc. 198, 339 (1982). [259] W. Tichy, B. Brügmann, M. Campanelli, and P. Diener : Binary black hole initial data for numerical general relativity based on post-Newtonian data, Phys. Rev. D 67, 064008 (2003). [260] A.A. Tsokaros and K. Uryu : Numerical method for binary black hole/neutron star initial data: Code test, Phys. Rev. D 75, 044026 (2007). [261] K. Uryu and Y. Eriguchi : New numerical method for constructing quasiequilibrium sequences of irrotational binary neutron stars in general relativity, Phys. Rev. D 61, 124023 (2000). [262] K. Uryu, M. Shibata, and Y. Eriguchi : Properties of general relativistic, irrotational binary neutron stars in close quasiequilibrium orbits: Polytropic equations of state, Phys. Rev. D 62, 104015 (2000). [263] K. Uryu, F. Limousin, J.L. Friedman, E. Gourgoulhon, and M. Shibata : Binary Neutron Stars: Equilibrium Models beyond Spatial Conformal Flatness, Phys. Rev. Lett. 97, 171101 (2006). [264] J.R. van Meter, J.G. Baker, M. Koppitz, D.I. Choi : How to move a black hole without excision: gauge conditions for the numerical evolution of a moving puncture, Phys. Rev. D 73, 124011 (2006). [265] R.M. Wald : General relativity, University of Chicago Press, Chicago (1984). [266] D. Walsh : Non-uniqueness in conformal formulations of the Einstein Constraints, preprint gr-qc/0610129. [267] J.A. Wheeler : Geometrodynamics and the issue of the final state, in Relativity, Groups and Topology, edited by C. DeWitt and B.S. DeWitt, Gordon and Breach, New York (1964), p. 316. [268] J.R. Wilson and G.J. Mathews : Relativistic hydrodynamics, in Frontiers in numerical relativity, edited by C.R. Evans, L.S. Finn and D.W. Hobill, Cambridge University Press, Cambridge (1989), p. 306.
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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 166 and 167: 166 Choice of foliation and spatial
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Page 180 and 181: 180 Evolution schemes Now the ∇-d
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Page 184 and 185: 184 Evolution schemes = 1 2 −∆
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Page 188 and 189: 188 Evolution schemes
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 214 and 215: 214 BIBLIOGRAPHY [226] M. Shibata :
Page 218 and 219: Index 1+log slicing, 161 3+1 formal
Page 220: 220 INDEX Ricci identity, 18 Ricci
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