Author: Ovidiu Cristinel Stoica
Publisher: Minkowski Institute Press
ISBN: 9781927763346
Category :
Languages : en
Pages : 140
Book Description
This Thesis deals with recent progress regarding singularities in General Relativity. Singularities are predicted by the theory, but raise difficult problems, because they make the usual equations to be plagued with infinities and to break down. To resolve some of these problems, extensions of differential geometry and of Einstein's equation to singularities were needed, and were constructed by the author. This generalization works easily at the Big-Bang singularity, which gained by this a description in terms of finite quantities which have both geometric and physical meaning. Moreover, a large class of Big-Bang singularities which are not necessarily homogeneous or isotropic is presented. In addition, these singularities satisfy the Weyl curvature hypothesis, emitted by Penrose to explain the arrow of time. The black hole singularities apparently are more difficult to deal with, but by applying a special procedure they turn out as well to admit a description in terms of finite quantities. In addition, these singularities exhibit a (geo)metric dimensional reduction, which might act as a regulator for the quantum fields, including for quantum gravity, in the high-energy limit. This opens the perspective of perturbative quantum gravity without modifying General Relativity.
Singular General Relativity
Author: Ovidiu Cristinel Stoica
Publisher: Minkowski Institute Press
ISBN: 9781927763346
Category :
Languages : en
Pages : 140
Book Description
This Thesis deals with recent progress regarding singularities in General Relativity. Singularities are predicted by the theory, but raise difficult problems, because they make the usual equations to be plagued with infinities and to break down. To resolve some of these problems, extensions of differential geometry and of Einstein's equation to singularities were needed, and were constructed by the author. This generalization works easily at the Big-Bang singularity, which gained by this a description in terms of finite quantities which have both geometric and physical meaning. Moreover, a large class of Big-Bang singularities which are not necessarily homogeneous or isotropic is presented. In addition, these singularities satisfy the Weyl curvature hypothesis, emitted by Penrose to explain the arrow of time. The black hole singularities apparently are more difficult to deal with, but by applying a special procedure they turn out as well to admit a description in terms of finite quantities. In addition, these singularities exhibit a (geo)metric dimensional reduction, which might act as a regulator for the quantum fields, including for quantum gravity, in the high-energy limit. This opens the perspective of perturbative quantum gravity without modifying General Relativity.
Publisher: Minkowski Institute Press
ISBN: 9781927763346
Category :
Languages : en
Pages : 140
Book Description
This Thesis deals with recent progress regarding singularities in General Relativity. Singularities are predicted by the theory, but raise difficult problems, because they make the usual equations to be plagued with infinities and to break down. To resolve some of these problems, extensions of differential geometry and of Einstein's equation to singularities were needed, and were constructed by the author. This generalization works easily at the Big-Bang singularity, which gained by this a description in terms of finite quantities which have both geometric and physical meaning. Moreover, a large class of Big-Bang singularities which are not necessarily homogeneous or isotropic is presented. In addition, these singularities satisfy the Weyl curvature hypothesis, emitted by Penrose to explain the arrow of time. The black hole singularities apparently are more difficult to deal with, but by applying a special procedure they turn out as well to admit a description in terms of finite quantities. In addition, these singularities exhibit a (geo)metric dimensional reduction, which might act as a regulator for the quantum fields, including for quantum gravity, in the high-energy limit. This opens the perspective of perturbative quantum gravity without modifying General Relativity.
Singular Null Hypersurfaces In General Relativity: Light-like Signals From Violent Astrophysical Events
Author: Peter A Hogan
Publisher: World Scientific
ISBN: 9814483370
Category : Science
Languages : en
Pages : 205
Book Description
This book presents a comprehensive and self-contained exposition of the mathematical theory of impulsive light-like signals in general relativity. Applications are provided in relativistic astrophysics, cosmology and alternative theories of gravity deduced from string theory. Cataclysmic astrophysical events give rise to impulsive light-like signals which can generally be decomposed into a thin shell of null matter and an impulsive gravitational wave. Several examples are considered in black hole physics, wave collisions and light-like boosts of compact gravitating sources.Graduate students and researchers in relativistic astrophysics, cosmology and string theory will find this book very useful.
Publisher: World Scientific
ISBN: 9814483370
Category : Science
Languages : en
Pages : 205
Book Description
This book presents a comprehensive and self-contained exposition of the mathematical theory of impulsive light-like signals in general relativity. Applications are provided in relativistic astrophysics, cosmology and alternative theories of gravity deduced from string theory. Cataclysmic astrophysical events give rise to impulsive light-like signals which can generally be decomposed into a thin shell of null matter and an impulsive gravitational wave. Several examples are considered in black hole physics, wave collisions and light-like boosts of compact gravitating sources.Graduate students and researchers in relativistic astrophysics, cosmology and string theory will find this book very useful.
General Relativity: Black hole astrophysics
Author: W. Israel
Publisher:
ISBN: 9780521138017
Category : Black holes (Astronomy)
Languages : en
Pages : 1064
Book Description
Publisher:
ISBN: 9780521138017
Category : Black holes (Astronomy)
Languages : en
Pages : 1064
Book Description
Geometry of Manifolds
Author:
Publisher: Academic Press
ISBN: 0080873278
Category : Mathematics
Languages : en
Pages : 287
Book Description
Geometry of Manifolds
Publisher: Academic Press
ISBN: 0080873278
Category : Mathematics
Languages : en
Pages : 287
Book Description
Geometry of Manifolds
Cosmological applications of singular hypersurfaces in general relativity
Author: Pablo Laguna-Castillo
Publisher:
ISBN:
Category : Cosmology
Languages : en
Pages : 376
Book Description
Publisher:
ISBN:
Category : Cosmology
Languages : en
Pages : 376
Book Description
Advanced General Relativity
Author: Claude Barrabès
Publisher: OUP Oxford
ISBN: 0191501883
Category : Science
Languages : en
Pages : 153
Book Description
This book is aimed at students making the transition from a first course on general relativity to a specialized subfield. It presents a variety of topics under the general headings of gravitational waves in vacuo and in a cosmological setting, equations of motion, and black holes, all having a clear physical relevance and a strong emphasis on space-time geometry. Each chapter could be used as a basis for an early postgraduate project for those who are exploring avenues into research in general relativity and who have already accumulated the required technical knowledge. The presentation of each chapter is research monograph style, rather than text book style, in order to impress on interested students the need to present their research in a clear and concise format. Students with advanced preparation in general relativity theory might find a treasure trove here.
Publisher: OUP Oxford
ISBN: 0191501883
Category : Science
Languages : en
Pages : 153
Book Description
This book is aimed at students making the transition from a first course on general relativity to a specialized subfield. It presents a variety of topics under the general headings of gravitational waves in vacuo and in a cosmological setting, equations of motion, and black holes, all having a clear physical relevance and a strong emphasis on space-time geometry. Each chapter could be used as a basis for an early postgraduate project for those who are exploring avenues into research in general relativity and who have already accumulated the required technical knowledge. The presentation of each chapter is research monograph style, rather than text book style, in order to impress on interested students the need to present their research in a clear and concise format. Students with advanced preparation in general relativity theory might find a treasure trove here.
The Singular Universe and the Reality of Time
Author: Roberto Mangabeira Unger
Publisher: Cambridge University Press
ISBN: 1107074061
Category : Science
Languages : en
Pages : 567
Book Description
Roberto Mangabeira Unger and Lee Smolin argue for a revolution in our cosmological ideas. Ideal for non-scientists, physicists and cosmologists.
Publisher: Cambridge University Press
ISBN: 1107074061
Category : Science
Languages : en
Pages : 567
Book Description
Roberto Mangabeira Unger and Lee Smolin argue for a revolution in our cosmological ideas. Ideal for non-scientists, physicists and cosmologists.
A First Course in General Relativity
Author: Bernard Schutz
Publisher: Cambridge University Press
ISBN: 0521887054
Category : Science
Languages : en
Pages : 411
Book Description
Second edition of a widely-used textbook providing the first step into general relativity for undergraduate students with minimal mathematical background.
Publisher: Cambridge University Press
ISBN: 0521887054
Category : Science
Languages : en
Pages : 411
Book Description
Second edition of a widely-used textbook providing the first step into general relativity for undergraduate students with minimal mathematical background.
Relativistic Cosmology
Author: George F. R. Ellis
Publisher: Cambridge University Press
ISBN: 0521381150
Category : Science
Languages : en
Pages : 637
Book Description
Surveying key developments and open issues in cosmology for graduate students and researchers, this book focuses on the general concepts and relations that underpin the standard model of the Universe. It also examines anisotropic and inhomogeneous models, and deeper issues, such as quantum cosmology and the multiverse proposal.
Publisher: Cambridge University Press
ISBN: 0521381150
Category : Science
Languages : en
Pages : 637
Book Description
Surveying key developments and open issues in cosmology for graduate students and researchers, this book focuses on the general concepts and relations that underpin the standard model of the Universe. It also examines anisotropic and inhomogeneous models, and deeper issues, such as quantum cosmology and the multiverse proposal.
The Large Scale Structure of Space-Time
Author: S. W. Hawking
Publisher: Cambridge University Press
ISBN: 1139810952
Category : Science
Languages : en
Pages : 406
Book Description
Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.
Publisher: Cambridge University Press
ISBN: 1139810952
Category : Science
Languages : en
Pages : 406
Book Description
Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.