| Author | : C. J. S. Clarke |
| Publisher | : Cambridge University Press |
| Total Pages | : 196 |
| Release | : 1993 |
| Genre | : 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 | : S. W. Hawking |
| Publisher | : Cambridge University Press |
| Total Pages | : 406 |
| Release | : 1975-02-27 |
| Genre | : 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 | : Marcus Kriele |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 444 |
| Release | : 2003-07-01 |
| Genre | : 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 | : John Earman |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 270 |
| Release | : 1995 |
| Genre | : 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 |
| Total Pages | : 279 |
| Release | : 2018 |
| Genre | : 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.
| Author | : Klaus Mainzer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 186 |
| Release | : 2013-03-14 |
| Genre | : Science |
| ISBN | : 1475743327 |
Time is fundamental to our experience, but remains mysterious. This book shows how philosophers and scientists have tried to grapple with this most extraordinary of ordinary phenomena. From the attempts of early astronomers to reconcile solar and lunar and terrestrial reckonings, to the huge expansions and contractions of time consciousness brought on by scientists as diverse as Newton, Darwin, and Einstein, this book shows how time is as much a matter of human choice as it is a matter of scientific precision.
| Author | : Roger Penrose |
| Publisher | : Vintage |
| Total Pages | : 307 |
| Release | : 2011-09-06 |
| Genre | : Science |
| ISBN | : 0307596745 |
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.
| Author | : Cesar Augusto Zen Vasconcellos |
| Publisher | : World Scientific |
| Total Pages | : 299 |
| Release | : 2019-12-26 |
| Genre | : Science |
| ISBN | : 9813277351 |
'The book concentrates attention on extended alternative theories of gravity and on the best astrophysical laboratories to probe the strong gravity-field regime: black holes, pulsars and neutron stars … Readers will likely share the satisfaction the editor and contributors say they experienced as they organized the book.'SirReadaLotFor more than a century, our understanding of gravitational physics was based on Albert Einstein's theory of General Relativity, which fundamentally changed our understanding of the Universe, its origin, and its evolutionary process. General Relativity accurately describes a large number of phenomena on very different scales. As such, it has been very well tested and its remarkable predictions are compatible with most experimental and observational data. However, the observational and experimental results compatible with General Relativity fall in its vast majority under the weak gravitational field regime. In recent years, discrepancies between the data and the corresponding predictions of General Relativity have been observed and have generated intense research activity. One of the most critical aspects of General Relativity is the presence of singularities in extreme physical situations. These discrepancies indicate that either the parameters of the theory must be modified in the regime of strong field gravity/high energy and large space-time curvature, or the theory itself should be modified. In this book, we focus our attention on extended alternative gravity theories and the best astrophysical laboratories to probe the strong field regime: black holes, pulsars, and neutron stars.
| Author | : Alessia Benedetta Platania |
| Publisher | : Springer |
| Total Pages | : 149 |
| Release | : 2018-09-20 |
| Genre | : Science |
| ISBN | : 3319987941 |
This book seeks to construct a consistent fundamental quantum theory of gravity, which is often considered one of the most challenging open problems in present-day physics. It approaches this challenge using modern functional renormalization group techniques, and attempts to realize the idea of “Asymptotic Safety” originally proposed by S. Weinberg. Quite remarkably, the book makes significant progress regarding both the fundamental aspects of the program and its phenomenological consequences. The conceptual developments pioneer the construction of a well-behaved functional renormalization group equation adapted to spacetimes with a preferred time-direction. It is demonstrated that the Asymptotic Safety mechanism persists in this setting and extends to many phenomenologically interesting gravity-matter systems. These achievements constitute groundbreaking steps towards bridging the gap between quantum gravity in Euclidean and Lorentzian spacetimes.The phenomenological applications cover core topics in quantum gravity, e.g. constructing a phenomenologically viable cosmological evolution based on quantum gravity effects in the very early universe, and analyzing quantum corrections to black holes forming from a spherical collapse.As a key feature, all developments are presented in a comprehensive and accessible way. This makes the work a timely and valuable guide into the rapidly evolving field of Asymptotic Safety.
