Euclidean Quantum Gravity

By: Gary W Gibbons (Editor), Stephen W Hawking (Editor)

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Paperback | 1 December 1992

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602 Pages

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The Euclidean approach to quantum gravity was initiated almost 15 years ago in an attempt to understand the difficulties raised by the spacetime singularities of classical general relativity which arise in the gravitational collapse of stars to form black holes and the entire universe in the Big Bang. An important motivation was to develop an approach capable of dealing with the non-linear, non-perturbative aspects of quantum gravity due to topologically non-trivial spacetimes. There are important links with a Riemannian geometry. Since its inception the theory has been applied to a number of important physical problems including the thermodynamic properties of black holes, quantum cosmology and the problem of the cosmological constant. It is currently at the centre of a great deal of interest. This is a collection of survey lectures and reprints of some important lectures on the Euclidean approach to quantum gravity in which one expresses the Feynman path integral as a sum over Riemannian metrics. As well as papers on the basic formalism there are sections on black holes, quantum cosmology, wormholes and gravitational instantons.

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Introduction
General Formalism
One-Loop Divergencies in the Theory of Gravitation	p. 3
The Path-Integral Approach to Quantum Gravity	p. 29
Euclidean Quantum Gravity	p. 73
Path Integrals and the Indefiniteness of the Gravitational Action	p. 102
Proof of the Positive Action Conjecture in Quantum Relativity	p. 112
Zeta Function Regularization of Path Integrals in Curved Spacetime	p. 114
The Conformal Rotation in Perturbative Gravity	p. 130
Quantum Tunneling and Negative Eigenvalues	p. 152
A Relation Between Volume, Mean Curvature and Diameter	p. 161
The Cosmological Constant is Probably Zero	p. 162
Black Holes
Particle Creation by Black Holes	p. 167
Path Integral Derivation of Black-Hole Radiance	p. 189
Black Holes and Thermal Green Functions	p. 205
Action Integrals and Partition Functions in Quantum Gravity	p. 233
Instability of Flat Space at Finite Temperature	p. 238
Thermal Stress Tensor in Static Einstein Spaces	p. 264
Quantum Stress Tensor in Schwarzschild Space-Time	p. 275
Quantum Cosmology
Cosmological Event Horizons, Thermodynamics and Particle Creation	p. 281
Gravitational Effects on and of Vacuum Decay	p. 295
Supercooled Phase Transitions in the Very Early Universe	p. 306
Wave Function of the Universe	p. 310
The Quantum State of the Universe	p. 326
Origin of Structure in the Universe	p. 346
Wormholes
Wormholes in Spacetime	p. 363
Axion-Induced Topology Change in Quantum Gravity and String Theory	p. 370
Why There is Nothing Rather than Something: A Theory of the Cosmological Constant	p. 388
Wormholes and the Cosmological Constant	p. 414
Wormholes in Spacetime and the Constants of Nature	p. 442
Wormholes in Spacetime and [actual symbol not reproducible]	p. 488
Gravitational Instantons
Asymptotically Flat Self-Dual Solutions to Euclidean Gravity	p. 497
Gravitational Multi-Instantons	p. 500
The Positive Action Conjecture and Asymptotically Euclidean Metrics in Quantum Gravity	p. 503
Polygons and Gravitons	p. 527
The Construction of ALE Spaces as Hyper-Kahler Quotients	p. 539
A Compact Rotating Gravitational Instanton	p. 558
Classification of Gravitational Instanton Symmetries	p. 562
Low Energy Scattering of Non-Abelian Monopoles	p. 582
Table of Contents provided by Blackwell. All Rights Reserved.

Euclidean Quantum Gravity

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Paperback

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