Euclidean Quantum Gravity

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World Scientific, 1993 - Science - 586 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 nonlinear, 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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Contents

GENERAL FORMALISM
x
OneLoop Divergencies in the Theory of Gravitation
69
The PathIntegral Approach to Quantum Gravity
69
Path Integrals and the Indefiniteness of the Gravitational Action
102
Proof of the Positive Action Conjecture in Quantum Relativity
112
The Conformal Rotation in Perturbative Gravity
143
Quantum Tunneling and Negative Eigenvalues
152
A Relation Between Volume Mean Curvature and Diameter
161
Gravitational Effects on and of Vacuum Decay
295
Supercooled Phase Transitions in the Very Early Universe
306
The Quantum State of the Universe
329
Origin of Structure in the Universe
347
Wormholes in Spacetime
366
A Theory
388
Wormholes and the Cosmological Constant
414
Wormholes in Spacetime and the Constants of Nature
442

Particle Creation by Black Holes
167
Black Holes and Thermal Green Functions
205
Action Integrals and Partition Functions in Quantum Gravity
233
Instability of Flat Space at Finite Temperature
257
Thermal Stress Tensor in Static Einstein Spaces
274
Cosmological Event Horizons Thermodynamics and Particle Creation
281
Asymptotically Flat SelfDual Solutions to Euclidean Gravity
497
The Positive Action Conjecture and Asymptotically Euclidean Metrics
503
Polygons and Gravitons
531
The Construction of ALE Spaces as HyperKahler Quotients
539
A Compact Rotating Gravitational Instanton
558
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About the author (1993)

Stephen William Hawking was born on January 8, 1942 in Oxford, England. As a student at Oxford University, Hawking studied Physics, and after three years was awarded a first class honors degree in Natural Science. After gaining a Ph.D. from Cambridge, Hawking became a Research Fellow, and later on a Professional Fellow at Gonville and Caius College. Widely regarded as one of the greatest theoretical physicists since Einstein, Hawking has held the post as Lucasian Professor of Mathematics at the University of Cambridge since 1979. Most famous for his research on black holes, he has written the books A Brief History of Time and Black Holes and Baby Universes, a collection of essays published in 1993. He also authored the books On the Shoulders of Giants, A Briefer History of Time, The Universe in a Nutshell, and The Grand Design. Hawking is also the author of numerous articles for scientific papers, has 12 honorary degrees and is a Fellow of The Royal Society and a Member of the U.S. National Academy of Sciences. Hawking was diagnosed with Lou Gehrig's disease in his early 20s and is now confined to a wheelchair. He uses a computer device to help him speak. Hawking holds a professorship at the University of Oxford. In 2015 Hawking's book A Brief History of Time, which he completed in 1984, became listed on the New York Times bestseller list.

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