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Author : Gregory L. Naber
Publisher : Cambridge University Press
Page : 196 pages
File Size : 11,3 MB
Release : 1988
Category : Mathematics
ISBN : 9780521336123
An elementary introduction to the geometrical methods and notions used in special and general relativity. Emphasizes the ideas concerned with structure of space-time that play a role in Penrose-Hawking singularity theorems.
Author : C. J. S. Clarke
Publisher : Cambridge University Press
Page : 196 pages
File Size : 32,55 MB
Release : 1993
Category : Science
ISBN : 9780521437967
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.
Author : Pankaj S. Joshi
Publisher : Cambridge University Press
Page : 0 pages
File Size : 45,85 MB
Release : 2012-09-20
Category : Science
ISBN : 9781107405363
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.
Author : S. W. Hawking
Publisher : Cambridge University Press
Page : 406 pages
File Size : 35,11 MB
Release : 1975-02-27
Category : Science
ISBN : 1139810952
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.
Author : Pankaj S. Joshi
Publisher : Cambridge University Press
Page : 284 pages
File Size : 34,5 MB
Release : 2007-12-13
Category : Science
ISBN : 9780521871044
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, first published in 2007, 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.
Author : Marcus Kriele
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 42,86 MB
Release : 2003-07-01
Category : Science
ISBN : 3540483543
One of the most of exciting aspects is the general relativity pred- tion of black holes and the Such Big Bang. predictions gained weight the theorems through Penrose. singularity pioneered In various by te- books on theorems general relativity singularity are and then presented used to that black holes exist and that the argue universe started with a To date what has big been is bang. a critical of what lacking analysis these theorems predict-’ We of really give a proof a typical singul- theorem and this ity use theorem to illustrate problems arising through the of possibilities violations" and "causality weak "shell very crossing These singularities". add to the problems weight of view that the point theorems alone singularity are not sufficient to the existence of predict physical singularities. The mathematical theme of the book In order to both solid gain a of and intuition understanding good for any mathematical theory, one,should to realise it as model of try a a fam- iar non-mathematical theories have had concept. Physical an especially the important on of and impact development mathematics, conversely various modern theories physical rather require sophisticated mathem- ics for their formulation. both and mathematics Today, physics are so that it is often difficult complex to master the theories in both very s- in the of jects. However, case differential pseudo-Riemannian geometry or the general relativity between and mathematics relationship physics is and it is therefore especially close, to from interd- possible profit an ciplinary approach.
Author : Sean M. Carroll
Publisher : Cambridge University Press
Page : 529 pages
File Size : 27,34 MB
Release : 2019-08-08
Category : Science
ISBN : 1108488390
An accessible introductory textbook on general relativity, covering the theory's foundations, mathematical formalism and major applications.
Author : Lior M. Burko
Publisher : Institute of Physics Publishing (GB)
Page : 552 pages
File Size : 27,39 MB
Release : 1997
Category : Science
ISBN :
The physics of black holes and spacetime singularities is now a well established area of research in gravitation theory. Over recent years researchers have begun to study the internal structure of black holes and spacetime singularities. This book is primarily the proceedings of a workshop devoted to the subject. The chapters are mainly written versions of the talks given at the workshop. However, the authors have written extended introductions to their contributions, so that a reader, well versed in gravitation theory, but unaware of the current research in this subfield, should be able to follow the text Several topics are considered by more than one author, bringing into the text different viewpoints on these topics. As a result, this book is suitable for graduate students who wish to familiarize themselves with the various aspects of the structure of black holes, and for researchers who wish to learn about advances in subfields other than their own. Topics covered include: the nature of thesingularities (both null and spacelike) and the spacetime inside black holes coupled to various matter fields in classical and semiclassical gravity, as well as in alternative gravity theories; the cosmic censorship hypothesis and its connection to black hole interiors; cosmological singularities and their relation with black hole singularities; and black hole entropy and evaporation.
Author : John Earman
Publisher : Oxford University Press, USA
Page : 270 pages
File Size : 28,56 MB
Release : 1995
Category : General relativity (Physics).
ISBN : 019509591X
Others hoped that peaceful coexistence with singularities could be achieved by proving a form of Roger Penrose's "cosmic censorship" hypothesis, which would place singularities safely inside black holes.
Author : Vladimir Belinski
Publisher : Cambridge University Press
Page : 279 pages
File Size : 46,23 MB
Release : 2018
Category : Science
ISBN : 1107047471
This book mathematically derives the theory underlying the Belinski-Khalatnikov-Lifshitz conjecture on the general solution of the Einstein equations with a cosmological singularity.