100 Years of Relativity Space-Time Structure: Einstein and Beyond ...

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172 P. Laguna17. C. Bona, C. Ledvinka, C. Palenzuela, and M. Zacek. General-covariant evolutionformalism for numerical relativity. Phys. Rev D, 68:041501, 2003.18. J.M. Bowen and J.W. York. Time-asymetric initial data for black holes andblack-hole collisions. Phys. Rev. D, 21:2047, 1980.19. S. Brandt and B. Bruegmann. Phys. Rev. Lett., 78:3606, 1997.20. O. Brodbeck, S. Frittelli, P. Huebner, and O.A. Reula. Einstein’s equationswith asymptotically stable constraint propagation. J. Math. Phys., 40:909,1999.21. B. Bruegmann, W. Tichy, and N. Jansen. Numerical simulation of orbitingblack holes. Phys. Rev. Lett., 92:211101, 2004.22. Cactus. www.cactuscode.org.23. M.W. Choptuik. Universality and scaling in gravitational collapse of a masslessscalar field. Phys. Rev. Lett., 70:9, 1993.24. G. Cook. Phys. Rev. D, 50:5025, 1994.25. G. Cook. Initial data for numerical relativity. Living Rev. Rel., 3:5, 2000.26. T. Damour, E. Gourgoulhon, and P. Grandclement. Circular orbits of corotatingbinary black holes: comparison between analytical and numerical results.Phys. Rev. D, 66:024007, 2002.27. D.R. Fiske, J.G. Baker, J.R. van Meter, D.-I. Choi, and J.M. Centrella. Wavezone extraction of gravitational radiation in three-dimensional numerical relativity.gr-qc/0503100, 2005.28. Jörg Frauendiener. Conformal infinity. Living Rev. Rel., 7:1, 2004.29. H. Friedrich. Hyperbolic reductions for einstein’s field equations. Class.Quantum Grav., 13:1451, 1996.30. D. Garfinkle. Harmonic coordinate methods for simulating generic singularities.Phys. Rev. D, 65:044029, 2002.31. E. Gourgoulhon, P. Grandclement, and Bonazzola S. Phys. Rev. D,65:044020, 2002.32. P. Grandclement, E. Gourgoulhon, and Bonazzola S. Phys. Rev D, 65:044021,2002.33. C. Gundlach. Critical phenomena in gravitational collapse. Living Rev. Rel.,2:4, 1999.34. C. Gundlach and J.M. Martin-Garcia. Symmetric hyperbolicity and consistentboundary conditions for second-order einstein equations. Phys. Rev. D,70:044032, 2004.35. C. Gundlach, J.M. Martin-Garcia, G. Calabrese, and I. Hinder. Constraintdamping in the z4 formulation and harmonic gauge. gr-qc/0504114, 2005.36. M. Holst, L. Lindblom, R. Owen, H.P. Pfeiffer, M.A. Scheel, and L.E. Kidder.Optimal constraint projection for hyperbolic evolution systems. Phys. Rev.D, 70:084017, 2004.37. B. Kelly, P. Laguna, K. Lockitch, J. Pullin, E. Schnetter, D. Shoemaker,and M Tiglio. A cure for unstable numerical evolutions of single black holes:adjusting the standard adm equations. Phys. Rev D, 64:084013, 2001.38. A.M. Khokhlov and I.D. Novikov. Gauge stability of 3+1 formulations ofgeneral relativity. Class. Quant. Grav., 19:827, 2002.39. L.E. Kidder, M.A. Scheel, and S.A. Teukolsky. Phys. Rev D, 64:064017, 2001.
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Published byWorld Scientific Publis
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viA. Ashtekarof space-time that eme
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viiiA. AshtekarGravitational waves
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xA. Ashtekarhappy, schizophrenic at
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xviContents9. Receiving Gravitation
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4 J. Stachel(2) the change over tim
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6 J. StachelFig. 2respectively. Fur
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8 J. Stachelof string theory, M-the
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10 J. StachelLogically, it would se
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12 J. Stachelupon by no (net) exter
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14 J. Stachelof the incompatibility
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16 J. Stachelis an important differ
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18 J. Stachelbetween physical conce
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20 J. Stachel10. Four-Dimensional F
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22 J. Stachelderivative of the metr
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24 J. Stachel(b) General relativity
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26 J. Stachelfour-dimensional analo
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28 J. Stachelply the lessons learne
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30 J. Stachelmanifold appropriate f
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32 J. Stachelwhich merely defines t
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34 J. Stacheldynamical process as a
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36 J. Stachel9. J. Stachel, Special
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Part IIEinstein’s UniverseRamific
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40 H. Nicolai• Higher dimensions
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42 H. Nicolaiadvance, and possibly
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44 H. NicolaiBianchi identities are
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46 H. NicolaiIt does not appear pos
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48 H. NicolaiThe other SL(2, R), of
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50 H. Nicolai3.1. BKL dynamics and
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52 H. Nicolaidegrees of freedom, th
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54 H. Nicolaiin the valley. The Ham
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56 H. NicolaiThe main feature of th
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58 H. Nicolai4. Basics of Kac Moody
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60 H. Nicolaifor indefinite A. It i
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62 H. NicolaiThe level l = 0 sector
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64 H. NicolaiConsequently, the repr
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66 H. Nicolaiwhere the abelian part
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68 H. Nicolaiconstant momenta Π yi
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70 H. Nicolaiσ-model side is suppo
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72 H. NicolaiReferences1. H.A. Buch
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74 H. Nicolai44. G. Neugebauer and
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CHAPTER 3THE NATURE OF SPACETIME SI
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78 A. D. Rendallspacetime to define
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80 A. D. RendallOne of the most imp
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82 A. D. Rendalltheorems was an elu
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84 A. D. Rendallsymmetric solution
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86 A. D. Rendallback into a curvatu
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88 A. D. Rendallspace and there are
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The Nature of Spacetime Singulariti
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CHAPTER 4BLACK HOLES - AN INTRODUCT
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Black Holes 95It follows that ˙v d
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Black Holes 973221100-1-1-2-200-5-3
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Black Holes 99calculation of the de
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Black Holes 101family of null geode
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Black Holes 105(3) Ω is positive o
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Black Holes 107In dimension 3 + 1 t
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Black Holes 109A fundamental theore
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Black Holes 111(4) The Kerr black h
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Black Holes 113˚g ab =˚g ab (x a
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Black Holes 115It is a folklore the
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Black Holes 117⃗x 4 = −⃗x 3
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Black Holes 119Work partially suppo
Page 139 and 140: Black Holes 121totically flat space
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Page 143 and 144: The Physical Basis of Black Hole As
Page 171 and 172: Probing Space-Time Through Numerica
Page 189: Probing Space-Time Through Numerica
Page 193 and 194: CHAPTER 7UNDERSTANDING OUR UNIVERSE
Page 195 and 196: Understanding Our Universe: Current
Page 223 and 224: CHAPTER 8WAS EINSTEIN RIGHT? TESTIN
Page 225 and 226: Was Einstein Right? 207We begin in
Page 227 and 228: Was Einstein Right? 20910 -810 -9E
Page 229 and 230: Was Einstein Right? 211On this 100t
Page 231 and 232: Was Einstein Right? 213The SME and
Page 233 and 234: Was Einstein Right? 215where d is t
Page 235 and 236: Was Einstein Right? 217of VLBI data
Page 237 and 238: Was Einstein Right? 219milliarcseco
Page 239 and 240: Was Einstein Right? 2215. Gravitati
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Was Einstein Right? 223be measured
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Was Einstein Right? 22510. J. G. Wi
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Was Einstein Right? 22761. C. M. Wi
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Receiving Gravitational Waves 229th
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Receiving Gravitational Waves 231gr
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Receiving Gravitational Waves 233Th
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Receiving Gravitational Waves 235We
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Receiving Gravitational Waves 23719
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Receiving Gravitational Waves 239th
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Receiving Gravitational Waves 241to
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Receiving Gravitational Waves 243In
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Receiving Gravitational Waves 245
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Receiving Gravitational Waves 247a
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Receiving Gravitational Waves 249ab
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Receiving Gravitational Waves 251Fi
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Receiving Gravitational Waves 253Eq
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Receiving Gravitational Waves 255In
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CHAPTER 10RELATIVITY IN THE GLOBAL
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Relativity in the Global Positionin
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Part IIIBeyond EinsteinUnifying Gen
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CHAPTER 11SPACETIME IN SEMICLASSICA
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Spacetime in Semiclassical Gravity
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CHAPTER 12SPACE TIME IN STRING THEO
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Space Time in String Theory 313limi
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Space Time in String Theory 315luti
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Space Time in String Theory 317In s
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Space Time in String Theory 319of t
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Space Time in String Theory 321an o
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Space Time in String Theory 323arbi
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Space Time in String Theory 325an e
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Space Time in String Theory 327in a
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Space Time in String Theory 329doma
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Space Time in String Theory 331a tu
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Space Time in String Theory 333bran
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Space Time in String Theory 335is a
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Space Time in String Theory 337thes
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Space Time in String Theory 339The
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Space Time in String Theory 341gene
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Space Time in String Theory 343are
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Space Time in String Theory 345tion
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Space Time in String Theory 34723.
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Space Time in String Theory 34955.
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Gravity, Geometry and the Quantum 3
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£¢¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡
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Loop Quantum Cosmology 383inflation
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Loop Quantum Cosmology 385gravitati
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Loop Quantum Cosmology 387Secondly,
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Loop Quantum Cosmology 389sically d
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Loop Quantum Cosmology 391states an
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Loop Quantum Cosmology 393represent
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Loop Quantum Cosmology 3954.2.1. Di
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Loop Quantum Cosmology 397question
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Loop Quantum Cosmology 399exist. Th
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Loop Quantum Cosmology 401in the ex
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Loop Quantum Cosmology 403λ max or
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Loop Quantum Cosmology 405This happ
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Loop Quantum Cosmology 407Loop quan
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Loop Quantum Cosmology 409to obtain
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Loop Quantum Cosmology 411familiar
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Loop Quantum Cosmology 41334. M. Bo
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CHAPTER 15CONSISTENT DISCRETE SPACE
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Consistent Discrete Space-Time 417v
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Consistent Discrete Space-Time 419I
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Consistent Discrete Space-Time 421a
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Consistent Discrete Space-Time 423F
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Consistent Discrete Space-Time 4250
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Consistent Discrete Space-Time 4272
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Consistent Discrete Space-Time 429i
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Consistent Discrete Space-Time 431a
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Consistent Discrete Space-Time 433n
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Consistent Discrete Space-Time 435t
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Consistent Discrete Space-Time 437w
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Consistent Discrete Space-Time 439f
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Consistent Discrete Space-Time 441(
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Consistent Discrete Space-Time 443R
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CHAPTER 16CAUSAL SETS ANDTHE DEEP S
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Causal Sets and the Deep Structure
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CHAPTER 17THE TWISTOR APPROACH TOSP
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The Twistor Approach to Space-Time
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INDEXσ models, 57, 65, 693+1 formu
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Index 509inflation, 383, 385-387, 4
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