Defining Gravitational Singularities In General Relativity
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Defining Gravitational Singularities In General Relativity
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Author :
language : en
Publisher:
Release Date : 2007
Defining Gravitational Singularities In General Relativity written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
Singularities have been a long-standing problem in general relativity. In all other fields of physics, singularities can be easily located and avoided; in general relativity, singularities have an impact on the creation of the manifold, but, by definition, are not even part of real spacetime. Moreover, all singularities in general relativity cannot be treated in the same manner; thus, the classification of singularities is essential in order to understand them. One important class of singularities is curvature singularities, which, in some cases, can be subclassified as central, shell focusing or shell crossing singularities. We propose to further classify curvature singularities as either gravitational or non-gravitational. In general relativity, a curvature singularity is ``located'' where the scalar invariants of the spacetime are undefined. The gradient field of a non-zero scalar invariant can then be calculated, and the end points of the associated integral curves can be determined. If integral curves are attracted to (i.e. intersect) the singularity, then it is a gravitational singularity; if the integral curves avoid the singularity, then it is a non-gravitational singularity. We will test our method by analysing several different spacetimes, including Friedman-Lemaitre-Robertson-Walker, Schwarzschild, self-similar Vaidya, self-similar Tolman-Bondi, non-self-similar Vaidya, and Kerr spacetimes. We find that in every case studied, the integral curves have specific end points, therefore they can be used to classify a curvature singularity as gravitational or non-gravitational. In Friedman-Lemaitre-Robertson-Walker and Schwarzschild spacetimes, we determined that the a(t) = 0 and r = 0 singularities, respectively, are gravitational singularities. In Vaidya and Tolman-Bondi spacetime, we determine that the massless shell focusing singularities are non-gravitational singularities and that the central singularities (which have mass) are gravitational singularities.
Defining Gravitational Singularities In General Relativity
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Author : James Howard Wurster
language : en
Publisher:
Release Date : 2008
Defining Gravitational Singularities In General Relativity written by James Howard Wurster and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
The Singularities As Ontological Limits Of The General Relativity
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Author : Nicolae Sfetcu
language : en
Publisher: Nicolae Sfetcu
Release Date : 2019-01-31
The Singularities As Ontological Limits Of The General Relativity written by Nicolae Sfetcu and has been published by Nicolae Sfetcu this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-31 with Science categories.
ESSAYS Collection The singularities from the general relativity resulting by solving Einstein's equations were and still are the subject of many scientific debates: Are there singularities in spacetime, or not? Big Bang was an initial singularity? If singularities exist, what is their ontology? Is the general theory of relativity a theory that has shown its limits in this case? In this essay I argue that there are singularities, and the general theory of relativity, as any other scientific theory at present, is not valid for singularities. But that does not mean, as some scientists think, that it must be regarded as being obsolete. After a brief presentation of the specific aspects of Newtonian classical theory and the special theory of relativity, and a brief presentation of the general theory of relativity, the chapter Ontology of General Relativity presents the ontological aspects of general relativity. The next chapter, Singularities, is dedicated to the presentation of the singularities resulting in general relativity, the specific aspects of the black holes and the event horizon, including the Big Bang debate as original singularity, and arguments for the existence of the singularities. In Singularity Ontology, I am talking about the possibilities of ontological framing of singularities in general and black holes in particular, about the hole argument highlighted by Einstein, and the arguments presented by scientists that there are no singularities and therefore that the general theory of relativity is in deadlock. In Conclusions I outline and summarize briefly the arguments that support my above views. CONTENTS Abstract Introduction Classical Theory and Special Relativity General Relativity (GR) 1 Ontology of General Relativity 2 Singularities Black Holes Event Horizon Big Bang Are there Singularities? 3 Ontology of Singularities Ontology of black holes The hole argument There are no singularities Conclusions Notes Bibliography
Global Aspects In Gravitation And Cosmology
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Author : Pankaj S. Joshi
language : en
Publisher: Oxford University Press, USA
Release Date : 1993
Global Aspects In Gravitation And Cosmology written by Pankaj S. Joshi and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Philosophy categories.
This book describes several basic results and applications of global aspects in gravitation theory and cosmology within the framework of Einstein's theory of gravity. Topics include results on the structure and topology of space-time, exact solutions to Einstein equations and singularities, the status of quantum gravity, and quantum effects near space-time singularities in strong curvature fields. Also covered are the global upper limits in cosmology on elementary particle masses which might constitute the dark matter of the universe. After discussing in detail the fundamental role played by global considerations in gravity and general relativity, the author points out the significant problems that remain: the nature and structure of space-time singularities, the cosmic censorship problem in black hole physics, and the issue of quantum effects in strong gravity fields. The author's treatment of gravitational collapse illustrates how powerfully-strong curvature naked singularities could result from the continual gravitational collapse of matter with several reasonable equations of state--including inflowing radiation, dust, or a perfect fluid. Students and mathematicians, astrophysicists, and physicists will find this theoretically rich book a landmark in relativity theory.
New Frontiers In Gravitational Collapse And Spacetime Singularities
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Author : Daniele Malafarina
language : en
Publisher: Springer Nature
Release Date :
New Frontiers In Gravitational Collapse And Spacetime Singularities written by Daniele Malafarina and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
The Analysis Of Space Time Singularities
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Author : C. J. S. Clarke
language : en
Publisher: Cambridge University Press
Release Date : 1993
The Analysis Of Space Time Singularities written by C. J. S. Clarke and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Science categories.
The different possible singularities are defined and the mathematical methods needed to extend the space-time are described in detail in this book. Results obtained (many appearing here for the first time) show that singularities are associated with a lack of smoothness in the Riemann tensor.
General Relativity And Gravitation
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Author : M. A. H. MacCallum
language : en
Publisher: CUP Archive
Release Date : 1987-09-24
General Relativity And Gravitation written by M. A. H. MacCallum and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-09-24 with Science categories.
Introduction To General Relativity Black Holes And Cosmology
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Author : Yvonne Choquet-Bruhat
language : en
Publisher: Oxford University Press
Release Date : 2015
Introduction To General Relativity Black Holes And Cosmology written by Yvonne Choquet-Bruhat and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.
General Relativity is a beautiful geometric theory, simple in its mathematical formulation but leading to numerous consequences with striking physical interpretations: gravitational waves, black holes, cosmological models, and so on. This introductory textbook is written for mathematics students interested in physics and physics students interested in exact mathematical formulations (or for anyone with a scientific mind who is curious to know more of the world we live in), recent remarkable experimental and observational results which confirm the theory are clearly described and no specialised physics knowledge is required. The mathematical level of Part A is aimed at undergraduate students and could be the basis for a course on General Relativity. Part B is more advanced, but still does not require sophisticated mathematics. Based on Yvonne Choquet-Bruhat's more advanced text, General Relativity and the Einstein Equations, the aim of this book is to give with precision, but as simply as possible, the foundations and main consequences of General Relativity. The first five chapters from General Relativity and the Einstein Equations have been updated with new sections and chapters on black holes, gravitational waves, singularities, and the Reissner-Nordstrom and interior Schwarzchild solutions. The rigour behind this book will provide readers with the perfect preparation to follow the great mathematical progress in the actual development, as well as the ability to model, the latest astrophysical and cosmological observations. The book presents basic General Relativity and provides a basis for understanding and using the fundamental theory.
Gravitational Collapse And Spacetime Singularities
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Author : Pankaj S. Joshi
language : en
Publisher: Cambridge University Press
Release Date : 2012-09-20
Gravitational Collapse And Spacetime Singularities written by Pankaj S. Joshi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-20 with Science categories.
Physical phenomena in astrophysics and cosmology involve gravitational collapse in a fundamental way. The final fate of a massive star when it collapses under its own gravity at the end of its life cycle is one of the most important questions in gravitation theory and relativistic astrophysics, and is the foundation of black hole physics. General relativity predicts that continual gravitational collapse gives rise to a space-time singularity. Quantum gravity may take over in such regimes to resolve the classical space-time singularity. This book investigates these issues, and shows how the visible ultra-dense regions arise naturally and generically as an outcome of dynamical gravitational collapse. It will be of interest to graduate students and academic researchers in gravitation physics, fundamental physics, astrophysics, and cosmology. It includes a detailed review of research into gravitational collapse, and several examples of collapse models are investigated in detail.
Gravity Black Holes And The Very Early Universe
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Author : Tai L. Chow
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-24
Gravity Black Holes And The Very Early Universe written by Tai L. Chow and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-24 with Science categories.
Here it is, in a nutshell: the history of one genius’s most crucial work – discoveries that were to change the face of modern physics. In the early 1900s, Albert Einstein formulated two theories that would forever change the landscape of physics: the Special Theory of Relativity and the General Theory of Relativity. Respected American academic Professor Tai Chow tells us the story of these discoveries. He details the basic ideas of Einstein, including his law of gravitation. Deftly employing his inimitable writing style, he goes on to explain the physics behind black holes, weaving into his account an explanation of the structure of the universe and the science of cosmology.