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

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CONTENTSPrefacevPart I: From Newton to EinsteinParadigm Shifts 11. Development of the Concepts of Space, Time and Space-Timefrom Newton to EinsteinJ. Stachel 3Part II: Einstein’s UniverseRamifications of General Relativity 372. Gravitational Billiards, Dualities and Hidden SymmetriesH. Nicolai 393. The Nature of Spaceime SingularitiesA. D. Rendall 764. Black Holes – An IntroductionP. T. Chruściel 935. The Physical Basis of Black Hole AstrophysicsR. H. Price 1246. Probing Space-Time Through Numerical SimulationsP. Laguna 1527. Understanding Our Universe: Current Status and Open IssuesT. Padmanabhan 1758. Was Einstein Right? Testing Relativity at the CentenaryC. M. Will 205xv
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Page 6 and 7: Published byWorld Scientific Publis
Page 8 and 9: viA. Ashtekarof space-time that eme
Page 10 and 11: viiiA. AshtekarGravitational waves
Page 12 and 13: xA. Ashtekarhappy, schizophrenic at
Page 18 and 19: xviContents9. Receiving Gravitation
Page 22 and 23: 4 J. Stachel(2) the change over tim
Page 24 and 25: 6 J. StachelFig. 2respectively. Fur
Page 26 and 27: 8 J. Stachelof string theory, M-the
Page 28 and 29: 10 J. StachelLogically, it would se
Page 30 and 31: 12 J. Stachelupon by no (net) exter
Page 32 and 33: 14 J. Stachelof the incompatibility
Page 34 and 35: 16 J. Stachelis an important differ
Page 36 and 37: 18 J. Stachelbetween physical conce
Page 38 and 39: 20 J. Stachel10. Four-Dimensional F
Page 40 and 41: 22 J. Stachelderivative of the metr
Page 42 and 43: 24 J. Stachel(b) General relativity
Page 44 and 45: 26 J. Stachelfour-dimensional analo
Page 46 and 47: 28 J. Stachelply the lessons learne
Page 48 and 49: 30 J. Stachelmanifold appropriate f
Page 50 and 51: 32 J. Stachelwhich merely defines t
Page 52 and 53: 34 J. Stacheldynamical process as a
Page 54 and 55: 36 J. Stachel9. J. Stachel, Special
Page 56 and 57: Part IIEinstein’s UniverseRamific
Page 58 and 59: 40 H. Nicolai• Higher dimensions
Page 60 and 61: 42 H. Nicolaiadvance, and possibly
Page 62 and 63: 44 H. NicolaiBianchi identities are
Page 64 and 65: 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
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Black Holes 121totically flat space
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Black Holes 12376. R.C. Myers and M
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The Physical Basis of Black Hole As
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Probing Space-Time Through Numerica
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CHAPTER 7UNDERSTANDING OUR UNIVERSE
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Understanding Our Universe: Current
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CHAPTER 8WAS EINSTEIN RIGHT? TESTIN
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Was Einstein Right? 207We begin in
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Was Einstein Right? 20910 -810 -9E
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Was Einstein Right? 211On this 100t
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Was Einstein Right? 213The SME and
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Was Einstein Right? 215where d is t
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Was Einstein Right? 217of VLBI data
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Was Einstein Right? 219milliarcseco
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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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