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Author: Gregory L. Naber
Publisher: Cambridge University Press
Published: 1988
Total Pages: 196
ISBN-13: 9780521336123
DOWNLOAD EBOOK →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
Published: 1993
Total Pages: 196
ISBN-13: 9780521437967
DOWNLOAD EBOOK →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
Published: 2007-12-13
Total Pages: 284
ISBN-13: 9780521871044
DOWNLOAD EBOOK →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: S. W. Hawking
Publisher: Cambridge University Press
Published: 1975-02-27
Total Pages: 406
ISBN-13: 1139810952
DOWNLOAD EBOOK →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: Marcus Kriele
Publisher: Springer Science & Business Media
Published: 2003-07-01
Total Pages: 444
ISBN-13: 3540483543
DOWNLOAD EBOOK →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
Published: 2019-08-08
Total Pages: 529
ISBN-13: 1108488390
DOWNLOAD EBOOK →An accessible introductory textbook on general relativity, covering the theory's foundations, mathematical formalism and major applications.
Author: John Earman
Publisher: Oxford University Press, USA
Published: 1995
Total Pages: 270
ISBN-13: 019509591X
DOWNLOAD EBOOK →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: Sean M. Carroll
Publisher: Cambridge University Press
Published: 2019-08-08
Total Pages: 530
ISBN-13: 1108775551
DOWNLOAD EBOOK →Spacetime and Geometry is an introductory textbook on general relativity, specifically aimed at students. Using a lucid style, Carroll first covers the foundations of the theory and mathematical formalism, providing an approachable introduction to what can often be an intimidating subject. Three major applications of general relativity are then discussed: black holes, perturbation theory and gravitational waves, and cosmology. Students will learn the origin of how spacetime curves (the Einstein equation) and how matter moves through it (the geodesic equation). They will learn what black holes really are, how gravitational waves are generated and detected, and the modern view of the expansion of the universe. A brief introduction to quantum field theory in curved spacetime is also included. A student familiar with this book will be ready to tackle research-level problems in gravitational physics.
Author: Vladimir Belinski
Publisher: Cambridge University Press
Published: 2017-10-26
Total Pages: 279
ISBN-13: 1107047471
DOWNLOAD EBOOK →This book mathematically derives the theory underlying the Belinski-Khalatnikov-Lifshitz conjecture on the general solution of the Einstein equations with a cosmological singularity.
Author: Roger Penrose
Publisher: Vintage
Published: 2011-09-06
Total Pages: 307
ISBN-13: 0307596745
DOWNLOAD EBOOK →From Nobel prize-winner Roger Penrose, this groundbreaking book is for anyone "who is interested in the world, how it works, and how it got here" (New York Journal of Books). Penrose presents a new perspective on three of cosmology’s essential questions: What came before the Big Bang? What is the source of order in our universe? And what cosmic future awaits us? He shows how the expected fate of our ever-accelerating and expanding universe—heat death or ultimate entropy—can actually be reinterpreted as the conditions that will begin a new “Big Bang.” He details the basic principles beneath our universe, explaining various standard and non-standard cosmological models, the fundamental role of the cosmic microwave background, the paramount significance of black holes, and other basic building blocks of contemporary physics. Intellectually thrilling and widely accessible, Cycles of Time is a welcome new contribution to our understanding of the universe from one of our greatest mathematicians and thinkers.
