## Gravitational Collapse and Spacetime Singularities

Author: Pankaj S. Joshi

Publisher: Cambridge University Press

ISBN: 1139468146

Category: Science

Page: N.A

View: 2687

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.

## The Large Scale Structure of Space-Time

Author: S. W. Hawking,G. F. R. Ellis

Publisher: Cambridge University Press

ISBN: 1139810952

Category: Science

Page: N.A

View: 6518

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.

## Euclidean Quantum Gravity

Author: G. W. Gibbons,Stephen W. Hawking

Publisher: World Scientific

ISBN: 9789810205164

Category: Science

Page: 586

View: 7236

The Euclidean approach to Quantum Gravity was initiated almost 15 years ago in an attempt to understand the difficulties raised by the spacetime singularities of classical general relativity which arise in the gravitational collapse of stars to form black holes and the entire universe in the Big Bang. An important motivation was to develop an approach capable of dealing with the nonlinear, non-perturbative aspects of quantum gravity due to topologically non-trivial spacetimes. There are important links with a Riemannian geometry. Since its inception the theory has been applied to a number of important physical problems including the thermodynamic properties of black holes, quantum cosmology and the problem of the cosmological constant. It is currently at the centre of a great deal of interest.This is a collection of survey lectures and reprints of some important lectures on the Euclidean approach to quantum gravity in which one expresses the Feynman path integral as a sum over Riemannian metrics. As well as papers on the basic formalism there are sections on Black Holes, Quantum Cosmology, Wormholes and Gravitational Instantons.

## The Cosmological Singularity

Author: Vladimir Belinski,Marc Henneaux

Publisher: Cambridge University Press

ISBN: 1108547990

Category: Science

Page: 263

View: 9930

Written for researchers focusing on general relativity, supergravity, and cosmology, this is a self-contained exposition of the structure of the cosmological singularity in generic solutions of the Einstein equations, and an up-to-date mathematical derivation of the theory underlying the Belinski–Khalatnikov–Lifshitz (BKL) conjecture on this field. Part I provides a comprehensive review of the theory underlying the BKL conjecture. The generic asymptotic behavior near the cosmological singularity of the gravitational field, and fields describing other kinds of matter, is explained in detail. Part II focuses on the billiard reformulation of the BKL behavior. Taking a general approach, this section does not assume any simplifying symmetry conditions and applies to theories involving a range of matter fields and space-time dimensions, including supergravities. Overall, this book will equip theoretical and mathematical physicists with the theoretical fundamentals of the Big Bang, Big Crunch, Black Hole singularities, the billiard description, and emergent mathematical structures.

## Noncompact Problems at the Intersection of Geometry, Analysis, and Topology

Proceedings of the Brezis-Browder Conference, Noncompact Variational Problems and General Relativity, October 14-18, 2001, Rutgers, the State University of New Jersey, New Brunswick, NJ

Author: Haim Brézis,Felix E. Browder,Abbas Bahri,Sergiu Klainerman,Michael Vogelius

Publisher: American Mathematical Soc.

ISBN: 0821836358

Category: Science

Page: 252

View: 5152

This proceedings volume contains articles from the conference held at Rutgers University in honor of Haim Brezis and Felix Browder, two mathematicians who have had a profound impact on partial differential equations, functional analysis, and geometry. The material is suitable for graduate students and researchers interested in problems in analysis and differential equations on noncompact manifolds.

## Hamiltonian Mechanics of Gauge Systems

Author: Lev V. Prokhorov,Sergei V. Shabanov

Publisher: Cambridge University Press

ISBN: 1139500902

Category: Science

Page: N.A

View: 3970

The principles of gauge symmetry and quantization are fundamental to modern understanding of the laws of electromagnetism, weak and strong subatomic forces and the theory of general relativity. Ideal for graduate students and researchers in theoretical and mathematical physics, this unique book provides a systematic introduction to Hamiltonian mechanics of systems with gauge symmetry. The book reveals how gauge symmetry may lead to a non-trivial geometry of the physical phase space and studies its effect on quantum dynamics by path integral methods. It also covers aspects of Hamiltonian path integral formalism in detail, along with a number of related topics such as the theory of canonical transformations on phase space supermanifolds, non-commutativity of canonical quantization and elimination of non-physical variables. The discussion is accompanied by numerous detailed examples of dynamical models with gauge symmetries, clearly illustrating the key concepts.

## Global Aspects in Gravitation and Cosmology

Author: Pankaj S. Joshi

Publisher: Oxford University Press on Demand

ISBN: 9780198500797

Category: Science

Page: 377

View: 5276

Basic to the entire theory and applications of black hole physics Global Aspects in Gravitation and Cosmology covers the topics needed to understand the current key issues in gravitation theory: cosmology and black holes. Emphasized is the basic theme that the very nature of the gravitationalfield is such that global features of space-time inevitably come into play whenever we try to understand and interpret this force in detail. After discussing the fundamental role played by global considerations in gravity and general relativity, Joshi points out the significant problems that remain.The key problem of which been the issue of quantum effects in strong gravity fields, an understanding of which is essential to formulate any quantum theory of gravity. This book will be beneficial to mathematicians and physicists.

## Quantum Field Theory in Curved Spacetime

Quantized Fields and Gravity

Author: Leonard Parker,David Toms

Publisher: Cambridge University Press

ISBN: 0521877873

Category: Science

Page: 455

View: 9182

Suitable for graduate students, this book develops quantum field theory in curved spacetime in a pedagogical style.

## The Cauchy Problem in General Relativity

Author: Hans Ringström

Publisher: European Mathematical Society

ISBN: 9783037190531

Category: Mathematics

Page: 294

View: 2638

"The general theory of relativity is a theory of manifolds equipped with Lorentz metrics and fields which describe the matter content. Einstein's equations equate the Einstein tensor (a curvature quantity associated with the Lorentz metric) with the stress energy tensor (an object constructed using the matter fields). In addition, there are equations describing the evolution of the matter. Using symmetry as a guiding principle, one is naturally led to the Schwarzschild and Friedmann-Lemaãitre-Robertson-Walker solutions, modelling an isolated system and the entire universe respectively. In a different approach, formulating Einstein's equations as an initial value problem allows a closer study of their solutions. This book first provides a definition of the concept of initial data and a proof of the correspondence between initial data and development. It turns out that some initial data allow non-isometric maximal developments, complicating the uniqueness issue. The second half of the book is concerned with this and related problems, such as strong cosmic censorship. The book presents complete proofs of several classical results that play a central role in mathematical relativity but are not easily accessible to those wishing to enter the subject. Prerequisites are a good knowledge of basic measure and integration theory as well as the fundamentals of Lorentz geometry. The necessary background from the theory of partial differential equations and Lorentz geometry is included."--Publisher's description.

## Gravitational Waves

Astrophysics and Cosmology

Author: Michele Maggiore

Publisher: Oxford University Press

ISBN: 0198570899

Category: Science

Page: 848

View: 4739

The two-volume book Gravitational Waves provides a comprehensive and detailed account of the physics of gravitational waves. While Volume 1 is devoted to the theory and experiments, Volume 2 discusses what can be learned from gravitational waves in astrophysics and in cosmology, by systematizing a large body of theoretical developments that have taken place over the last decades. The second volume also includes a detailed discussion of the first direct detections of gravitational waves. In the author's typical style, the theoretical results are generally derived afresh, clarifying or streamlining the existing derivations whenever possible, and providing a coherent and consistent picture of the field. The first volume of Gravitational Waves , which appeared in 2007, has established itself as the standard reference in the field. The scientific community has eagerly awaited this second volume. The recent direct detection of gravitational waves makes the topics in this book particularly timely.

## Progress in Mathematical Relativity, Gravitation and Cosmology

Proceedings of the Spanish Relativity Meeting ERE2012, University of Minho, Guimarães, Portugal, September 3-7, 2012

Author: Alfonso García-Parrado,Filipe C. Mena,Filipe Moura,Estelita Vaz

Publisher: Springer Science & Business Media

ISBN: 3642401570

Category: Mathematics

Page: 485

View: 4599

This book contains contributions from the Spanish Relativity Meeting, ERE 2012, held in Guimarães, Portugal, September 2012. It features more than 70 papers on a range of topics in general relativity and gravitation, from mathematical cosmology, numerical relativity and black holes to string theory and quantum gravity. Under the title "Progress in Mathematical Relativity, Gravitation and Cosmology," ERE 2012 was attended by an exceptional international list of over a hundred participants from the five continents and over forty countries. ERE is organized every year by one of the Spanish or Portuguese groups working in this area and is supported by the Spanish Society of Gravitation and Relativity (SEGRE). This book will be of interest to researchers in mathematics and physics.

## The Story of Collapsing Stars

Black Holes, Naked Singularities, and the Cosmic Play of Quantum Gravity

Author: Pankaj S. Joshi

Publisher: Oxford University Press, USA

ISBN: 0199686769

Category: Nature

Page: 225

View: 8157

This book describes some of the most fascinating occurences in the universe - black holes and space-time singularities. These arise when massive stars reach the end of their life cycle and collapse and shrink under their own gravity as they exhaust their supply of internal nuclear fuel. A star that was once millions of kilometers in size shrinks to a pinprick smaller than the dot on an "i". This is the space-time singularity, an extreme region of the universewhere densities, temperatures, and all other physical quantities take arbitrarily large values. According to Einstein's theory of gravity, the singularity is either covered within an event horizon, thusgiving a black hole, or it can be a visible naked singularity. The final fate of the star depends on its internal structure. In cases of the singularity being visible to faraway observers in the universe, we have the possibility to witness the workings of quantum gravity effects. Such observational signatures related to how the gravity and quantum may operate together could help us formulate the quantum gravity theory, a long cherished dream of physicists. Thus these issues are found to beintimately related to our search for the Unification of Physics, understanding all the basic forces in nature in a single theoretical framework.

## Theory and Experiment in Gravitational Physics

Author: Clifford M. Will

Publisher: Cambridge University Press

ISBN: 9780521439732

Category: Science

Page: 380

View: 7161

This is a revised edition of a classic and highly regarded book, first published in 1981, describing the status of theory and experiment in general relativity. The book provides all the necessary theoretical background, and covers all the important experimental tests. A new chapter has been added to cover recent important experimental tests, and the bibliography has been brought right up to date. Reviews of the previous edition: ' … consolidates much of the literature on experimental gravity and should be invaluable to researchers in gravitation …' Science ' … a concise and meaty book … and a most useful reference work … researchers and serious students of gravitation should be pleased with it …' Nature

## Re-Thinking Time at the Interface of Physics and Philosophy

The Forgotten Present

Author: Albrecht von Müller,Thomas Filk

Publisher: Springer

ISBN: 3319104462

Category: Science

Page: 274

View: 2512

The current volume of the Parmenides Series “On Thinking” addresses our deepest and most personal experience of the world, the experience of “the present,” from a modern perspective combining physics and philosophy. Many prominent researchers have contributed articles to the volume, in which they present models and express their opinions on and, in some cases, also their skepticism about the subject and how it may be (or may not be) addressed, as well as which aspects they consider most relevant in this context. While Einstein might have once hoped that “the present” would find its place in the theory of general relativity, in a later discussion with Carnap he expressed his disappointment that he was never able to achieve this goal. This collection of articles provides a unique overview of different modern approaches, representing not only a valuable summary for experts, but also a nearly inexhaustible source of profound and novel ideas for those who are simply interested in this question.

## Questioning the Foundations of Physics

Which of Our Fundamental Assumptions Are Wrong?

Author: Anthony Aguirre,Brendan Foster,Zeeya Merali

Publisher: Springer

ISBN: 3319130455

Category: Science

Page: 274

View: 1497

The essays in this book look at way in which the fundaments of physics might need to be changed in order to make progress towards a unified theory. They are based on the prize-winning essays submitted to the FQXi essay competition “Which of Our Basic Physical Assumptions Are Wrong?”, which drew over 270 entries. As Nobel Laureate physicist Philip W. Anderson realized, the key to understanding nature’s reality is not anything “magical”, but the right attitude, “the focus on asking the right questions, the willingness to try (and to discard) unconventional answers, the sensitive ear for phoniness, self-deception, bombast, and conventional but unproven assumptions.” The authors of the eighteen prize-winning essays have, where necessary, adapted their essays for the present volume so as to (a) incorporate the community feedback generated in the online discussion of the essays, (b) add new material that has come to light since their completion and (c) to ensure accessibility to a broad audience of readers with a basic grounding in physics. The Foundational Questions Institute, FQXi, catalyzes, supports, and disseminates research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality, but unlikely to be supported by conventional funding sources.

## Classical Solutions in Quantum Field Theory

Solitons and Instantons in High Energy Physics

Author: Erick J. Weinberg

Publisher: Cambridge University Press

ISBN: 0521114632

Category: Science

Page: 326

View: 1878

Overview of classical solutions and their consequences in quantum field theory, high energy physics and cosmology for graduates and researchers.

## Status of general relativity

Author: William B. Bonnor

Publisher: N.A

ISBN: N.A

Category: Science

Page: 38

View: 7481

## Rotating Relativistic Stars

Author: John L. Friedman,Nikolaos Stergioulas

Publisher: Cambridge University Press

ISBN: 1107310601

Category: Science

Page: N.A

View: 1253

The masses of neutron stars are limited by an instability to gravitational collapse and an instability driven by gravitational waves limits their spin. Their oscillations are relevant to x-ray observations of accreting binaries and to gravitational wave observations of neutron stars formed during the coalescence of double neutron-star systems. This volume includes more than forty years of research to provide graduate students and researchers in astrophysics, gravitational physics and astronomy with the first self-contained treatment of the structure, stability and oscillations of rotating neutron stars. This monograph treats the equations of stellar equilibrium; key approximations, including slow rotation and perturbations of spherical and rotating stars; stability theory and its applications, from convective stability to the r-mode instability; and numerical methods for computing equilibrium configurations and the nonlinear evolution of their oscillations. The presentation of fundamental equations, results and applications is accessible to readers who do not need the detailed derivations.

## Gravity and Strings

Author: Tomás Ortín

Publisher: Cambridge University Press

ISBN: 1316239578

Category: Science

Page: N.A

View: 4247

Self-contained and comprehensive, this definitive new edition of Gravity and Strings is a unique resource for graduate students and researchers in theoretical physics. From basic differential geometry through to the construction and study of black-hole and black-brane solutions in quantum gravity - via all the intermediate stages - this book provides a complete overview of the intersection of gravity, supergravity, and superstrings. Now fully revised, this second edition covers an extensive array of topics, including new material on non-linear electric-magnetic duality, the electric-tensor formalism, matter-coupled supergravity, supersymmetric solutions, the geometries of scalar manifolds appearing in 4- and 5-dimensional supergravities, and much more. Covering reviews of important solutions and numerous solution-generating techniques, and accompanied by an exhaustive index and bibliography, this is an exceptional reference work.

## The Quantization of Gravity

Author: Claus Gerhardt

Publisher: Springer

ISBN: 3319773712

Category: Science

Page: 200

View: 3494

​A unified quantum theory incorporating the four fundamental forces of nature is one of the major open problems in physics. The Standard Model combines electro-magnetism, the strong force and the weak force, but ignores gravity. The quantization of gravity is therefore a necessary first step to achieve a unified quantum theory. In this monograph a canonical quantization of gravity has been achieved by quantizing a geometric evolution equation resulting in a gravitational wave equation in a globally hyperbolic spacetime. Applying the technique of separation of variables we obtain eigenvalue problems for temporal and spatial self-adjoint operators where the temporal operator has a pure point spectrum with eigenvalues $\lambda_i$ and related eigenfunctions, while, for the spatial operator, it is possible to find corresponding eigendistributions for each of the eigenvalues $\lambda_i$, if the Cauchy hypersurface is asymptotically Euclidean or if the quantized spacetime is a black hole with a negative cosmological constant. The hyperbolic equation then has a sequence of smooth solutions which are products of temporal eigenfunctions and spatial eigendistributions. Due to this "spectral resolution" of the wave equation quantum statistics can also be applied to the quantized systems. These quantum statistical results could help to explain the nature of dark matter and dark energy.