3+1 formalism and bases of numerical relativity - LUTh ...
3+1 formalism and bases of numerical relativity - LUTh ... 3+1 formalism and bases of numerical relativity - LUTh ...
212 BIBLIOGRAPHY [195] S. Nissanke : Post-Newtonian freely specifiable initial data for binary black holes in numerical relativity, Phys. Rev. D 73, 124002 (2006). [196] N. Ó Murchadha and J.W. York : Initial-value problem of general relativity. I. General formulation and physical interpretation, Phys. Rev. D 10, 428 (1974). [197] R. Oechslin, H.-T. Janka and A. Marek : Relativistic neutron star merger simulations with non-zero temperature equations of state I. Variation of binary parameters and equation of state, Astron. Astrophys., submitted [preprint: astro-ph/0611047]. [198] R. Oechslin, K. Uryu, G. Poghosyan, and F. K. Thielemann : The Influence of Quark Matter at High Densities on Binary Neutron Star Mergers, Mon. Not. Roy. Astron. Soc. 349, 1469 (2004). [199] K. Oohara, T. Nakamura, and M. Shibata : A Way to 3D Numerical Relativity, Prog. Theor. Phys. Suppl. 128, 183 (1997). [200] L.I. Petrich, S.L Shapiro and S.A. Teukolsky : Oppenheimer-Snyder collapse with maximal time slicing and isotropic coordinates, Phys. Rev. D 31, 2459 (1985). [201] H.P. Pfeiffer : The initial value problem in numerical relativity, in Proceedings Miami Waves Conference 2004 [preprint gr-qc/0412002]. [202] H.P. Pfeiffer and J.W. York : Extrinsic curvature and the Einstein constraints, Phys. Rev. D 67, 044022 (2003). [203] H.P. Pfeiffer and J.W. York : Uniqueness and Nonuniqueness in the Einstein Constraints, Phys. Rev. Lett. 95, 091101 (2005). [204] T. Piran : Methods of Numerical Relativity, in Rayonnement gravitationnel / Gravitation Radiation, edited by N. Deruelle and T. Piran, North Holland, Amsterdam (1983), p. 203. [205] E. Poisson : A Relativist’s Toolkit, The Mathematics of Black-Hole Mechanics, Cambridge University Press, Cambridge (2004); http://www.physics.uoguelph.ca/poisson/toolkit/ [206] F. Pretorius : Numerical relativity using a generalized harmonic decomposition, Class. Quantum Grav. 22, 425 (2005). [207] F. Pretorius : Evolution of Binary Black-Hole Spacetimes, Phys. Rev. Lett. 95, 121101 (2005). [208] F. Pretorius : Simulation of binary black hole spacetimes with a harmonic evolution scheme, Class. Quantum Grav. 23, S529 (2006). [209] T. Regge and C. Teitelboim : Role of surface integrals in the Hamiltonian formulation of general relativity, Ann. Phys. (N.Y.) 88, 286 (1974). [210] B. Reimann and B. Brügmann : Maximal slicing for puncture evolutions of Schwarzschild and Reissner-Nordström black holes, Phys. Rev. D 69, 044006 (2004).
BIBLIOGRAPHY 213 [211] B.L. Reinhart : Maximal foliations of extended Schwarzschild space, J. Math. Phys. 14, 719 (1973). [212] A.D. Rendall : Theorems on Existence and Global Dynamics for the Einstein Equations, Living Rev. Relativity 8, 6 (2005); http://www.livingreviews.org/lrr-2005-6 [213] O.A. Reula : Hyperbolic Methods for Einstein’s Equations, Living Rev. Relativity 1, 3 (1998); http://www.livingreviews.org/lrr-1998-3 [214] O. Reula : Strong Hyperbolicity, lecture at the VII Mexican School on Gravitation and Mathematical Physics (Playa del Carmen, November 26 - December 2, 2006, Mexico); available at http://www.smf.mx/ ∼ dgfm-smf/EscuelaVII [215] M. Saijo : The Collapse of Differentially Rotating Supermassive Stars: Conformally Flat Simulations, Astrophys. J. 615, 866 (2004). [216] M. Saijo : Dynamical bar instability in a relativistic rotational core collapse, Phys. Rev. D 71, 104038 (2005). [217] O. Sarbach and M. Tiglio : Boundary conditions for Einstein’s field equations: mathematical and numerical analysis, J. Hyper. Diff. Equat. 2, 839 (2005). [218] G. Schäfer : Equations of Motion in the ADM Formalism, lectures at Institut Henri Poincaré, Paris (2006), http://www.luth.obspm.fr/IHP06/ [219] M.A. Scheel, H.P. Pfeiffer, L. Lindblom, L.E. Kidder, O. Rinne, and S.A. Teukolsky : Solving Einstein’s equations with dual coordinate frames, Phys. Rev. D 74, 104006 (2006). [220] R. Schoen and S.-T. Yau : Proof of the Positive Mass Theorem. II., Commun. Math. Phys. 79, 231 (1981). [221] Y. Sekiguchi and M. Shibata : Axisymmetric collapse simulations of rotating massive stellar cores in full general relativity: Numerical study for prompt black hole formation, Phys. Rev. D 71, 084013 (2005). [222] S.L. Shapiro and S.A. Teukolsky : Collisions of relativistic clusters and the formation of black holes, Phys. Rev. D 45, 2739 (1992). [223] M. Shibata : Relativistic formalism for computation of irrotational binary stars in quasiequilibrium states, Phys. Rev. D 58, 024012 (1998). [224] M. Shibata : 3D Numerical Simulations of Black Hole Formation Using Collisionless Particles, Prog. Theor. Phys. 101, 251 (1999). [225] M. Shibata : Fully General Relativistic Simulation of Merging Binary Clusters — Spatial Gauge Condition, Prog. Theor. Phys. 101, 1199 (1999).
- Page 162 and 163: 162 Choice of foliation and spatial
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- Page 188 and 189: 188 Evolution schemes
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- Page 192 and 193: 192 Lie derivative
- Page 194 and 195: 194 Conformal Killing operator and
- Page 196 and 197: 196 Conformal Killing operator and
- Page 198 and 199: 198 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 214 and 215: 214 BIBLIOGRAPHY [226] M. Shibata :
- 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
212 BIBLIOGRAPHY<br />
[195] S. Nissanke : Post-Newtonian freely specifiable initial data for binary black holes in <strong>numerical</strong><br />
<strong>relativity</strong>, Phys. Rev. D 73, 124002 (2006).<br />
[196] N. Ó Murchadha <strong>and</strong> J.W. York : Initial-value problem <strong>of</strong> general <strong>relativity</strong>. I. General<br />
formulation <strong>and</strong> physical interpretation, Phys. Rev. D 10, 428 (1974).<br />
[197] R. Oechslin, H.-T. Janka <strong>and</strong> A. Marek : Relativistic neutron star merger simulations with<br />
non-zero temperature equations <strong>of</strong> state I. Variation <strong>of</strong> binary parameters <strong>and</strong> equation <strong>of</strong><br />
state, Astron. Astrophys., submitted [preprint: astro-ph/0611047].<br />
[198] R. Oechslin, K. Uryu, G. Poghosyan, <strong>and</strong> F. K. Thielemann : The Influence <strong>of</strong> Quark<br />
Matter at High Densities on Binary Neutron Star Mergers, Mon. Not. Roy. Astron. Soc.<br />
349, 1469 (2004).<br />
[199] K. Oohara, T. Nakamura, <strong>and</strong> M. Shibata : A Way to 3D Numerical Relativity, Prog.<br />
Theor. Phys. Suppl. 128, 183 (1997).<br />
[200] L.I. Petrich, S.L Shapiro <strong>and</strong> S.A. Teukolsky : Oppenheimer-Snyder collapse with maximal<br />
time slicing <strong>and</strong> isotropic coordinates, Phys. Rev. D 31, 2459 (1985).<br />
[201] H.P. Pfeiffer : The initial value problem in <strong>numerical</strong> <strong>relativity</strong>, in Proceedings Miami<br />
Waves Conference 2004 [preprint gr-qc/0412002].<br />
[202] H.P. Pfeiffer <strong>and</strong> J.W. York : Extrinsic curvature <strong>and</strong> the Einstein constraints, Phys. Rev.<br />
D 67, 044022 (2003).<br />
[203] H.P. Pfeiffer <strong>and</strong> J.W. York : Uniqueness <strong>and</strong> Nonuniqueness in the Einstein Constraints,<br />
Phys. Rev. Lett. 95, 091101 (2005).<br />
[204] T. Piran : Methods <strong>of</strong> Numerical Relativity, in Rayonnement gravitationnel / Gravitation<br />
Radiation, edited by N. Deruelle <strong>and</strong> T. Piran, North Holl<strong>and</strong>, Amsterdam (1983), p. 203.<br />
[205] E. Poisson : A Relativist’s Toolkit, The Mathematics <strong>of</strong> Black-Hole Mechanics, Cambridge<br />
University Press, Cambridge (2004);<br />
http://www.physics.uoguelph.ca/poisson/toolkit/<br />
[206] F. Pretorius : Numerical <strong>relativity</strong> using a generalized harmonic decomposition, Class.<br />
Quantum Grav. 22, 425 (2005).<br />
[207] F. Pretorius : Evolution <strong>of</strong> Binary Black-Hole Spacetimes, Phys. Rev. Lett. 95, 121101<br />
(2005).<br />
[208] F. Pretorius : Simulation <strong>of</strong> binary black hole spacetimes with a harmonic evolution<br />
scheme, Class. Quantum Grav. 23, S529 (2006).<br />
[209] T. Regge <strong>and</strong> C. Teitelboim : Role <strong>of</strong> surface integrals in the Hamiltonian formulation <strong>of</strong><br />
general <strong>relativity</strong>, Ann. Phys. (N.Y.) 88, 286 (1974).<br />
[210] B. Reimann <strong>and</strong> B. Brügmann : Maximal slicing for puncture evolutions <strong>of</strong> Schwarzschild<br />
<strong>and</strong> Reissner-Nordström black holes, Phys. Rev. D 69, 044006 (2004).
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