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The five lectures presented in this volume address very timely
mathematical problems in relativity and cosmology. "Part I" is
devoted to the initial value and evolution problems of the Einstein
equations. Especially it deals with the
Einstein-Yang-Mills-Boltzmann system, fluid models with finite or
infinite conductivity, global evolution of a new (two-phase) model
for gravitational collapse and the structure of maximal,
asymptotically flat, vacuum solutions of the constraint equations
which have the additional property of containing trapped surfaces.
"Part II" focuses on geometrical-topological problems in relativity
and cosmology: on the role of cosmic censorship for the global
structure of the Einstein-Maxwell equations and on the mathematical
structure of quantum conformal superspace.
This book is written in a pedagogical style intelligible for
graduate students. It reviews recent progress in black-hole and
wormhole theory and in mathematical cosmology within the framework
of Einstein's field equations and beyond, including quantum
effects. This collection of essays, written by leading scientists
of long standing reputation, should become an indispensable source
for future research.
This book is written in a pedagogical style intelligible for
graduate students. It reviews recent progress in black-hole and
wormhole theory and in mathematical cosmology within the framework
of Einstein's field equations and beyond, including quantum
effects. This collection of essays, written by leading scientists
of long standing reputation, should become an indispensable source
for future research.
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.
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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