Download or read book Singularities in Gravitational Systems written by Daniel Benest and published by Springer. This book was released on 2008-01-11 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos theory plays an important role in modern physics and related sciences, but -, the most important results so far have been obtained in the study of gravitational systems applied to celestial mechanics. The present set of lectures introduces the mathematical methods used in the theory of singularities in gravitational systems, reviews modeling techniques for the simulation of close encounters and presents the state of the art about the study of diffusion of comets, wandering asteroids, meteors and planetary ring particles. The book will be of use to researchers and graduate students alike.
Download or read book Singularities in Gravitational Systems written by Daniel Benest and published by Springer. This book was released on 2009-09-02 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos theory plays an important role in modern physics and related sciences, but -, the most important results so far have been obtained in the study of gravitational systems applied to celestial mechanics. The present set of lectures introduces the mathematical methods used in the theory of singularities in gravitational systems, reviews modeling techniques for the simulation of close encounters and presents the state of the art about the study of diffusion of comets, wandering asteroids, meteors and planetary ring particles. The book will be of use to researchers and graduate students alike.
Download or read book Gravitational Collapse and Spacetime Singularities written by Pankaj S. Joshi and published by Cambridge University Press. This book was released on 2012-09-20 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Singularity Theory and Gravitational Lensing written by Arlie O. Petters and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is the first to develop a mathematical theory of gravitational lensing. The theory applies to any finite number of deflector planes and highlights the distinctions between single and multiple plane lensing. Introductory material in Parts I and II present historical highlights and the astrophysical aspects of the subject. Part III employs the ideas and results of singularity theory to put gravitational lensing on a rigorous mathematical foundation.
Download or read book The Cosmological Singularity written by Vladimir Belinski and published by Cambridge University Press. This book was released on 2018 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book mathematically derives the theory underlying the Belinski-Khalatnikov-Lifshitz conjecture on the general solution of the Einstein equations with a cosmological singularity.
Download or read book Gravitation Cosmology and Cosmic Ray Physics written by National Research Council and published by National Academies Press. This book was released on 1986-02-01 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The singularities as ontological limits of the general relativity written by Nicolae Sfetcu and published by Nicolae Sfetcu. This book was released on 2019-01-31 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Defining Gravitational Singularities in General Relativity written by and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Gravitation written by Charles W. Misner and published by Princeton University Press. This book was released on 2017-10-24 with total page 1332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spacetime physics -- Physics in flat spacetime -- The mathematics of curved spacetime -- Einstein's geometric theory of gravity -- Relativistic stars -- The universe -- Gravitational collapse and black holes -- Gravitational waves -- Experimental tests of general relativity -- Frontiers
Download or read book The Analysis of Space Time Singularities written by C. J. S. Clarke and published by Cambridge University Press. This book was released on 1993 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Ergodic Theory and Dynamical Systems I written by KATOK and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bangs Crunches Whimpers and Shrieks written by John Earman and published by Oxford University Press, USA. This book was released on 1995 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Gravity Realities of conscious world of singularity written by Aloysius Sebastian and published by Aloysius Sebastian. This book was released on 2019-03-19 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of my theories in physics. The main attractions of these theories are some revolutionary thoughts in science like "Gravity has a finite range", the “Big bang scenery inside a black hole” and “particle singularity”. It states that the wave nature of a particle is the product of work done by a particle in a medium. The wave is creating in a medium. Also it states that information can travel faster than light and it can travel in backward direction too. The similarities of the Big bang singularity and the Black hole singularity. In the chapter time travel I am intend to say that, a time traveler cannot create an incident in past or future, he can only meet the information. The chapter 2 and 3 are about the Theory of gravitation. There I am trying to explain the range of gravitational field. For that I have found a new constant "A". It was derivate from the equations of Sir Isaac Newton, the very famous Albert Einstein and many others. According to my Theory and equations, the gravity of an independent object will Zero at a certain distance. Newton and Einstein was discus about the gravitational force of attraction between two objects and I am explaining the range of the gravitational field of an individual object. I cannot believe that, if I have a steel ball with a weight of one kilogram in my hand and someone says to me that, it has an infinite range of gravity, it is out of my logic. I believe in physics and my physics is my surroundings. My observations on surrounding are giving me all my answers. Chapter 1 is discussing the dual nature of a particle. If I am telling somewhere, a "Particle is at rest". People say that, it is impossible to observe a particle at rest. I can't believe that, because we can conclude there is a particle at rest in several occasions. While we are projecting an atom, the particle inside the atom is at rest. If we go tinier particle like a proton, the quarks inside it will be at rest. When the proton is moving, the quark inside it is moving, but it is an inertial motion. It is like, when we are travelling in a bus, we are also moving with the bus. But we don't have any roll in that motion; we are at an inertial motion. Also I asked peoples in some discussions that, what is the nature of a particle at rest? They told me that is showing particle nature at rest. But, then why they are showing dual nature when they are moving?? Here is the presence of a medium, and the waves are creating in the medium. I believe that it is same in microscopic world and macroscopic world. Because of the laws of universe are always same for everything. In the third theory I am explaining about this. We are living in a conscious world where the information can travel faster than light. Everything in our universe is conscious about its state. The light from sun needs 8.20 minutes to reach earth, but we can see the sun at a blink of our eyes, and that describes the speed of information. We are watching a sun which was 8 minutes before. Here the information leads us to the past. Hope you will enjoy reading my book.
Download or read book Spacetime and Geometry written by Sean M. Carroll and published by Cambridge University Press. This book was released on 2019-08-08 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introductory textbook on general relativity, covering the theory's foundations, mathematical formalism and major applications.
Download or read book New Frontiers in Gravitational Collapse and Spacetime Singularities written by Daniele Malafarina and published by Springer. This book was released on 2024-05-21 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book collects a series of articles to review the advances that have been made in the field of gravitational collapse in general relativity and alternative theories of gravity in the past few years. Many approaches to black hole and singularity formation in general relativity and beyond have been proposed over the last few decades. The importance of collapse models is that they provide natural thought experiments where to test the behavior and properties of a variety of approaches to general relativity and its implications for ultra-compact objects in the universe.
Download or read book Chaotic Worlds from Order to Disorder in Gravitational N Body Dynamical Systems written by B.A. Steves and published by Springer Science & Business Media. This book was released on 2006-09-22 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the recent NATO Advanced Study Institute "Chaotic Worlds: From Order to Disorder in Gravitational N-Body Dynamical Systems", this state of the art textbook, written by internationally renowned experts, provides an invaluable reference volume for all students and researchers in gravitational n-body systems. The contributions are especially designed to give a systematic development from the fundamental mathematics which underpin modern studies of ordered and chaotic behaviour in n-body dynamics to their application to real motion in planetary systems. This volume presents an up-to-date synoptic view of the subject.
Download or read book Gravitational Lenses written by P. Schneider and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: Light observed from distant objects is found to be deflected by the gravitational field of massive objects near the line of sight - an effect predicted by Einstein in his first paper setting forth the general theory of relativity, and confirmed by Eddington soon afterwards. If the source of the light is sufficiently distant and bright, and if the intervening object is massive enough and near enough to the line of sight, the gravitational field acts like a lens, focusing the light and producing one or more bright images of the source. This book, by renowned researchers in the field, begins by discussing the basic physics behind gravitational lenses: the optics of curved space-time. It then derives the appropriate equations for predicting the properties of these lenses. In addition, it presents up-to-date observational evidence for gravitational lenses and describes the particular properties of the observed cases. The authors also discuss applications of the results to problems in cosmology.
