Three Roads To Quantum Gravity

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SUGGESTIONS FOR FURTHER READING 239 entropy conjecture', hep-th/9905177, Journal of High-Energy Physics, 9907 (1999) 0004; R. Bousso, `Holography in general space-times', hepth/9906022, Journal of High-Energy Physics 9906 (1999) 028. A related theorem was proved in E. Flanagan, D. Marolf and R. Wald, hep-th/ 9908070. F. Markopoulou and I proposed a background independent version in `Holography in a quantum spacetime', hep-th/9910146. In `The strong and weak holographic principles', hep-th/0003056 I review the arguments for and against the different versions of the principle. CHAPTER 13 The view of the relationship between loop quantum gravity and string theory is based on L. Smolin, `Strings as perturbations of evolving spin networks', hep-th/9801022; L. Smolin, `A candidate for a background independent formulation of M theory', hep-th/9903166; L. Smolin, `The cubic matrix model and a duality between strings and loops', hep-th/ 006137. There is an extensive literature on black holes in both string theory and loop quantum gravity. A sample of string theory papers is: A. Strominger and C. Vafa, Physics Letters B379 (1996) 99, hep-th/9601029; C.V. Johnson, R.R. Khuri and R.C. Myers, Physics Letters B378 (1996) 78, hep-th/9603061; J.M. Maldacena and A. Strominger, Physical Review Letters 77 (1996) 428, hep-th/9603060; C.G. Callan and J.M. Maldacena, Nuclear Physics B472 (1996) 591, hep-th/9602043; G.T. Horowitz and A. Strominger, Physical Review Letters 77 (1996) 2368, hep-th/9602051. A sample of papers on black holes in loop quantum gravity is: Carlo Rovelli, `Black hole entropy from loop quantum gravity', gr-qc/9603063, Physical Review Letters 77 (1996) 3288; Marcelo Barreira, Mauro Carfora and Carlo Rovelli, `Physics with nonperturbative quantum gravity: radiation from a quantum black hole', gr-qc/9603064, General Relativity and Gravity 28 (1996) 1293; Kirill Krasnov, `On quantum statistical mechanics of a Schwarzschild black hole', gr-qc/9605047, General Relativity and Gravity 30 (1998) 53; Kirill Krasnov, `Quantum geometry and thermal radiation from black holes', gr-qc/9710006, Classical and Quantum Gravity 16 (1999) 563; A. Ashtekar, J. Baez and K. Krasnov, `Quantum geometry of isolated horizons and black hole entropy', gr-qc/ 0005126; A. Ashtekar, J. Baez, A. Corichi and K. Krasnov, `Quantum geometry and black hole entropy', gr-qc/9710007, Physical Review Letters 80 (1998) 904. Non-commutative geometry is introduced in the book by Alain Connes, Non-commutative Geometry (Academic Press, 1994).
240 THREE ROADS TO QUANTUM GRAVITY CHAPTER 14 The material described here is mostly related to my book, Life of the Cosmos. The discussion of space is drawn from S. Kauffman and L. Smolin, `Combinatorial dynamics in quantum gravity', hep-th/9809161.
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I POINTS OF DEPARTURE
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CHAPTER 2 .........................
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II WHAT WE HAVE LEARNED
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CHAPTER 7 .........................
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CHAPTER 9 .........................
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CHAPTER 11 ........................
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CHAPTER 12 ........................
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THE HOLOGRAPHIC PRINCIPLE 171 gener
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THE HOLOGRAPHIC PRINCIPLE 173 FIGUR
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THE HOLOGRAPHIC PRINCIPLE 175 the g
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CHAPTER 13 ........................
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HOW TO WEAVE A STRING 181 thing!" I
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HOW TO WEAVE A STRING 183 other. Th
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HOW TO WEAVE A STRING 185 What is r
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HOW TO WEAVE A STRING 187 for a pic
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Page 216 and 217: EPILOGUE: .........................
Page 218 and 219: EPILOGUE: 209 And quantum gravity i
Page 220 and 221: EPILOGUE: 211 of systems containing
Page 222 and 223: POSTSCRIPT 213 These cosmic rays ar
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Page 226 and 227: POSTSCRIPT 217 light, which is the
Page 228 and 229: POSTSCRIPT 219 This is good news in
Page 230 and 231: POSTSCRIPT 221 But there is a secon
Page 232 and 233: POSTSCRIPT 223 Chopin Soo and Marti
Page 234 and 235: POSTSCRIPT 225 speed of light with
Page 236 and 237: GLOSSARY 227 cannot be greater than
Page 238 and 239: GLOSSARY 229 event In relativity th
Page 240 and 241: GLOSSARY 231 Newton's gravitational
Page 242 and 243: GLOSSARY 233 spin The angular momen
Page 244 and 245: SUGGESTIONS FOR FURTHER READING ...
Page 246 and 247: SUGGESTIONS FOR FURTHER READING 237
Page 250 and 251: INDEX .............................
Page 252 and 253: INDEX 243 black hole, 70, 73±4, 17
Page 254 and 255: INDEX 245 black hole formation, 189
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