Singular General Relativity - Theory.nipne.ro

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Introduction Problems of <strong>General</strong> <strong>Relativity</strong> There are two big problems in <strong>General</strong> <strong>Relativity</strong>: 1 It predicts the occurrence of singularities (Penrose, 1965; Hawking, 1966a; Hawking, 1966b; Hawking, 1967; Hawking & Penrose, 1970). 2 The attempts to quantize gravity seem to fail, because it is perturbatively nonrenormalizable (’t Hooft & Veltman, 1974; Goroff & Sagnotti, 1986). 4 / 142
Introduction Problems of <strong>General</strong> <strong>Relativity</strong> There are two big problems in <strong>General</strong> <strong>Relativity</strong>: 1 It predicts the occurrence of singularities (Penrose, 1965; Hawking, 1966a; Hawking, 1966b; Hawking, 1967; Hawking & Penrose, 1970). 2 The attempts to quantize gravity seem to fail, because it is perturbatively nonrenormalizable (’t Hooft & Veltman, 1974; Goroff & Sagnotti, 1986). Are these problems signs that we should give up <strong>General</strong> <strong>Relativity</strong> in favor of more radical approaches (superstrings, loop quantum gravity etc.)? 5 / 142
Page 1 and 2: Singular G
Page 3: Introduction Problems of Ge
Page 7 and 8: Introduction Problems of Ge
Page 9 and 10: Introduction Singular</stro
Page 19 and 20: Two types of singularities Introduc
Page 21 and 22: Two types of singularities Introduc
Page 23 and 24: Introduction What is wrong with sin
Page 29 and 30: Examples of singularities Examples
Page 39 and 40: The mathematics of singularities Re
Page 41 and 42: The mathematics of singularities De
Page 43 and 44: The mathematics of singularities <s
Page 49 and 50: The Koszul object The mathematics o
Page 51 and 52: The Koszul object The mathematics o
Page 53 and 54: The mathematics of singularities Th
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The mathematics of singularities Th
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The mathematics of singularities Co
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The mathematics of singularities Ex
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Einstein’s equation on semi-regul
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Einstein’s equation on semi-regul
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Friedmann-Lemaître-Robertson-Walke
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Black hole singularities Schwarzsch
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Black hole singularities Schwarzsch
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Black hole singularities Reissner-N
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Global hyperbolicity and informatio
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Global hyperbolicity and informatio
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The mathematics of singularities 2
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Dimensional reduction and QFT Is di
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Dimensional reduction and QFT Quant
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What if the singularities are not a
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References Physical Review Letters,
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References Riemannian (1+d)-Dim Spa
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References Proc. Roy. Soc. London S
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References Dream-land with Classic
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References Stoica, O. C. 2012d. Qua
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