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 ...
204 BIBLIOGRAPHY [75] M. Campanelli, C. O. Lousto, and Y. Zlochower : Spinning-black-hole binaries: The orbital hang-up, Phys. Rev. D 74, 041501(R) (2006). [76] M. Campanelli, C. O. Lousto, and Y. Zlochower : Spin-orbit interactions in black-hole binaries, Phys. Rev. D 74, 084023 (2006). [77] M. Cantor: The existence of non-trivial asymptotically flat initial data for vacuum spacetimes, Commun. Math. Phys. 57, 83 (1977). [78] M. Cantor : Some problems of global analysis on asymptotically simple manifolds, Compositio Mathematica 38, 3 (1979); available at http://www.numdam.org/item?id=CM 1979 38 1 3 0 [79] S.M. Carroll : Spacetime and Geometry: An Introduction to General Relativity, Addison Wesley (Pearson Education), San Fransisco (2004); http://pancake.uchicago.edu/ ∼ carroll/grbook/ [80] B. Carter : Outer curvature and conformal geometry of an imbedding, J. Geom. Phys. 8, 53 (1992). [81] B. Carter : Basic brane theory, Class. Quantum Grav. 9, S19 (1992). [82] B. Carter : Extended tensorial curvature analysis for embeddings and foliations, Contemp. Math. 203, 207 (1997). [83] M. Caudill, G.B. Cook, J.D. Grigsby, and H.P. Pfeiffer : Circular orbits and spin in black-hole initial data, Phys. Rev. D 74, 064011 (2006). [84] M.W. Choptuik : Numerical Analysis for Numerical Relativists, lecture at the VII Mexican School on Gravitation and Mathematical Physics, Playa del Carmen (Mexico), 26 November - 1 December 2006 [2]; available at http://laplace.physics.ubc.ca/People/matt/Teaching/06Mexico/ [85] M.W. Choptuik, E.W. Hirschmann, S.L. Liebling, and F. Pretorius : An axisymmetric gravitational collapse code, Class. Quantum Grav. 20, 1857 (2003). [86] Y. Choquet-Bruhat : New elliptic system and global solutions for the constraints equations in general relativity, Commun. Math. Phys. 21, 211 (1971). [87] Y. Choquet-Bruhat and R. Geroch : Global Aspects of the Cauchy Problem in General Relativity, Commun. Math. Phys. 14, 329 (1969). [88] Y. Choquet-Bruhat and J.W. York : The Cauchy Problem, in General Relativity and Gravitation, one hundred Years after the Birth of Albert Einstein, Vol. 1, edited by A. Held, Plenum Press, New York (1980), p. 99. [89] Y. Choquet-Bruhat and D. Christodoulou : Elliptic systems of Hs,δ spaces on manifolds which are Euclidean at infinity, Acta Math. 146, 129 (1981)
BIBLIOGRAPHY 205 [90] Y. Choquet-Bruhat and T. Ruggeri : Hyperbolicity of the 3+1 system of Einstein equations, Commun. Math. Phys. 89, 269 (1983). [91] Y. Choquet-Bruhat, J. Isenberg, and J.W. York : Einstein constraints on asymptotically Euclidean manifolds, Phys. Rev. D 61, 084034 (2000). [92] P.T. Chru´sciel : On angular momentum at spatial infinity, Class. Quantum Grav. 4, L205 (1987). [93] P.T. Chru´sciel and H. Friedrich (Eds.), The Einstein Equations and the Large Scale Behavior of Gravitational Fields — 50 years of the Cauchy Problem in General Relativity, Birkhäuser Verlag, Basel (2004). [94] G.B. Cook : Initial data for numerical relativity, Living Rev. Relativity 3, 5 (2000); http://www.livingreviews.org/lrr-2000-5 [95] G.B. Cook and H.P. Pfeiffer : Excision boundary conditions for black-hole initial data, Phys. Rev. D 70, 104016 (2004). [96] G.B. Cook and M.A. Scheel : Well-Behaved Harmonic Time Slices of a Charged, Rotating, Boosted Black Hole, Phys. Rev. D 56, 4775 (1997). [97] G.B. Cook, S.L. Shapiro and S.A. Teukolsky : Testing a simplified version of Einstein’s equations for numerical relativity, Phys. Rev. D 53, 5533 (1996). [98] J. Corvino : Scalar curvature deformation and a gluing construction for the Einstein constraint equations, Commun. Math. Phys. 214, 137 (2000). [99] E. Cotton : Sur les variétés à trois dimensions, Annales de la faculté des sciences de Toulouse Sér. 2, 1, 385 (1899); available at http://www.numdam.org/item?id=AFST 1899 2 1 4 385 0 [100] R. Courant and D. Hilbert : Methods of Mathematical Physics; vol. II : Partial Differential Equations, Interscience, New York (1962). [101] S. Dain : Elliptic systems, in Analytical and Numerical Approaches to Mathematical Relativity, edited by J. Frauendiener, D.J.W. Giulini, and V. Perlick, Lect. Notes Phys. 692, Springer, Berlin (2006), p. 117. [102] T. Damour : Coalescence of two spinning black holes: An effective one-body approach, Phys. Rev. D 64, 124013 (2001). [103] T. Damour : Advanced General Relativity, lectures at Institut Henri Poincaré, Paris (2006), available at http://www.luth.obspm.fr/IHP06/ [104] T. Damour, E. Gourgoulhon, and P. Grandclément : Circular orbits of corotating binary black holes: comparison between analytical and numerical results, Phys. Rev. D 66, 024007 (2002).
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- Page 188 and 189: 188 Evolution schemes
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- Page 192 and 193: 192 Lie derivative
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- Page 200 and 201: 200 BIBLIOGRAPHY [13] A. Anderson a
- Page 202 and 203: 202 BIBLIOGRAPHY [43] T.W. Baumgart
- 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 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
204 BIBLIOGRAPHY<br />
[75] M. Campanelli, C. O. Lousto, <strong>and</strong> Y. Zlochower : Spinning-black-hole binaries: The orbital<br />
hang-up, Phys. Rev. D 74, 041501(R) (2006).<br />
[76] M. Campanelli, C. O. Lousto, <strong>and</strong> Y. Zlochower : Spin-orbit interactions in black-hole<br />
binaries, Phys. Rev. D 74, 084023 (2006).<br />
[77] M. Cantor: The existence <strong>of</strong> non-trivial asymptotically flat initial data for vacuum spacetimes,<br />
Commun. Math. Phys. 57, 83 (1977).<br />
[78] M. Cantor : Some problems <strong>of</strong> global analysis on asymptotically simple manifolds, Compositio<br />
Mathematica 38, 3 (1979);<br />
available at http://www.numdam.org/item?id=CM 1979 38 1 3 0<br />
[79] S.M. Carroll : Spacetime <strong>and</strong> Geometry: An Introduction to General Relativity, Addison<br />
Wesley (Pearson Education), San Fransisco (2004);<br />
http://pancake.uchicago.edu/ ∼ carroll/grbook/<br />
[80] B. Carter : Outer curvature <strong>and</strong> conformal geometry <strong>of</strong> an imbedding, J. Geom. Phys. 8,<br />
53 (1992).<br />
[81] B. Carter : Basic brane theory, Class. Quantum Grav. 9, S19 (1992).<br />
[82] B. Carter : Extended tensorial curvature analysis for embeddings <strong>and</strong> foliations, Contemp.<br />
Math. 203, 207 (1997).<br />
[83] M. Caudill, G.B. Cook, J.D. Grigsby, <strong>and</strong> H.P. Pfeiffer : Circular orbits <strong>and</strong> spin in<br />
black-hole initial data, Phys. Rev. D 74, 064011 (2006).<br />
[84] M.W. Choptuik : Numerical Analysis for Numerical Relativists, lecture at the VII Mexican<br />
School on Gravitation <strong>and</strong> Mathematical Physics, Playa del Carmen (Mexico), 26<br />
November - 1 December 2006 [2];<br />
available at http://laplace.physics.ubc.ca/People/matt/Teaching/06Mexico/<br />
[85] M.W. Choptuik, E.W. Hirschmann, S.L. Liebling, <strong>and</strong> F. Pretorius : An axisymmetric<br />
gravitational collapse code, Class. Quantum Grav. 20, 1857 (2003).<br />
[86] Y. Choquet-Bruhat : New elliptic system <strong>and</strong> global solutions for the constraints equations<br />
in general <strong>relativity</strong>, Commun. Math. Phys. 21, 211 (1971).<br />
[87] Y. Choquet-Bruhat <strong>and</strong> R. Geroch : Global Aspects <strong>of</strong> the Cauchy Problem in General<br />
Relativity, Commun. Math. Phys. 14, 329 (1969).<br />
[88] Y. Choquet-Bruhat <strong>and</strong> J.W. York : The Cauchy Problem, in General Relativity <strong>and</strong><br />
Gravitation, one hundred Years after the Birth <strong>of</strong> Albert Einstein, Vol. 1, edited by A.<br />
Held, Plenum Press, New York (1980), p. 99.<br />
[89] Y. Choquet-Bruhat <strong>and</strong> D. Christodoulou : Elliptic systems <strong>of</strong> Hs,δ spaces on manifolds<br />
which are Euclidean at infinity, Acta Math. 146, 129 (1981)
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