S. W. HAWKING: The Event Horizon B. CARTER: Black Hole Equilibrium States J. M. ВARDEEN: Timelike and Null Geodesies In the Kerr Metric J. M. ВARDEEN: Rapidly Rotating Start, Disks, and Black Holes H. GURSKY: Observations of Galactic X-ray Sources I. D. NOVIKOV and K. S. THORNE: Black Hole Astrophysics R. RUFFINI: On the Energetics of Black Holes.

Battelle rencontres: 1967 lectures in mathematics and physics

Einstein’s general theory of relativity requires a curved space for the description of the physical world. If one wishes to go beyond superficial discussions of the physical relations involved, one needs to set up precise equations for handling curved space.Показать полностьюEinstein’s general theory of relativity requires a curved space for the description of the physical world. If one wishes to go beyond superficial discussions of the physical relations involved, one needs to set up precise equations for handling curved space. The well-established mathematical technique that accomplishes this is clearly described in this classic book by Nobel Laureate P.A.M. Dirac. Based on a series of lectures given by Dirac at Florida State University, and intended for the advanced undergraduate,General Theory of Relativitycomprises thirty-five compact chapters that take the reader point-by-point through the necessary steps for understanding general relativity.

This book will be useful for all readers. It provides good information about Diffuse Matter in the Universe.

This book definely matches a lot of students. Provides information about principles of Relativity — Special and General Theory.

In der vorliegenden Ausarbeitung von vier Vortragen, die ich an der Universitat Princeton im Mai 1921 gehal- gehalten habe, wollte ich die Hauptgedanken und mathematische Methoden der Relativitatstheorie »zusammenfassen.Показать полностьюIn der vorliegenden Ausarbeitung von vier Vortragen, die ich an der Universitat Princeton im Mai 1921 gehal- gehalten habe, wollte ich die Hauptgedanken und mathematische Methoden der Relativitatstheorie »zusammenfassen. Dabei habe ich mich bemuht, alles weniger Wesentliche wegzulassen, das Grundsatzliche aber doch so zu behandeln, da? das Ganze als Einfuhrung fur alle diejenigen dienen kann, welche die Elemente der hoheren Mathematik beherrschen, aber nicht allzuviel Zeit und Muhe auf den Gegenstand verwenden wollen. Auf Vollstandigkeit kann diese kurze Darlegung selbstverstandlich keinen Anspruch machen, zumal ich die feineren, mehr mathematisch interessanten Entwicklungen, welche sich auf Variationsrechnung grunden, nicht behandelt habe. Mein Hauptziel war es, das Grundsatzliche in dem ganzen Gedankengang der Theorie klar hervortreten zu lassen.

The present book is intended, as far as possible, to give an exact insight into the theory of Relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics.Показать полностьюThe present book is intended, as far as possible, to give an exact insight into the theory of Relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics. The work presumes a standard of education corresponding to that of a university matriculation examination, and, despite the shortness of the book, a fair amount of patience and force of will on the part of the reader. The author has spared himself no pains in his endeavour to present the main ideas in the simplest and most intelligible form, and on the whole, in the sequence and connection in which they actually originated. In the interest of clearness, it appeared to me inevitable that I should repeat myself frequently, without paying the slightest attention to the elegance of the presentation. I adhered scrupulously to the precept of that brilliant theoretical physicist L. Boltzmann, according to whom matters of elegance ought to be left to the tailor and to the cobbler. I make no pretence of having withheld from the reader difficulties which are inherent to the subject. On the other hand, I have purposely treated the empirical physical foundations of the theory in a "step?motherly" fashion, so that readers unfamiliar with physics may not feel like the wanderer who was unable to see the forest for the trees. May the book bring some one a few happy hours of suggestive thought!

Physical phenomena in the Riemannian space of arbitrary dimensionality D= D' + 1 (D1 = integer) are analyzed. It is noted, that with the dimensionality of physical space of the observable Metagalaxy D = 3 + 1 very important physical features are connected, which distinguish that value of D from the others.Показать полностьюPhysical phenomena in the Riemannian space of arbitrary dimensionality D= D' + 1 (D1 = integer) are analyzed. It is noted, that with the dimensionality of physical space of the observable Metagalaxy D = 3 + 1 very important physical features are connected, which distinguish that value of D from the others. However, this does not mean that the dimensionality of the physical space of the whole Universe must coincide with the value D = 3 + 1. This conclusion is confirmed by the geometric interpretation of supergravity and Kaluza-Klein theory. Different models of compactification and dimensional reduction of physical space and models of Metagalaxy formation in multidimensional spaces are reviewed.

Asymptotic structure of space-time

This volume introduces the application of two-component spinor calculus and fibre-bundle theory to complex general relativity. A review of basic and important topics is presented, such as two-component spinor calculus, conformal gravity, twistor spaces for Minkowski space-time and for curved space-time, Penrose transform for gravitation, the global theory of the Dirac operator in Riemannian four-manifolds, various definitions of twistors in curved space-time and the recent attempt by Penrose to define twistors as spin-3/2 charges in Ricci-flat space-time.Показать полностьюThis volume introduces the application of two-component spinor calculus and fibre-bundle theory to complex general relativity. A review of basic and important topics is presented, such as two-component spinor calculus, conformal gravity, twistor spaces for Minkowski space-time and for curved space-time, Penrose transform for gravitation, the global theory of the Dirac operator in Riemannian four-manifolds, various definitions of twistors in curved space-time and the recent attempt by Penrose to define twistors as spin-3/2 charges in Ricci-flat space-time. Original results include some geometrical properties of complex space-times with nonvanishing torsion, the Dirac operator with locally supersymmetric boundary conditions, the application of spin-lowering and spin-raising operators to elliptic boundary value problems, and the Dirac and Rarita — Schwinger forms of spin-3/2 potentials applied in real Riemannian four-manifolds with boundary. This book is written for students and research workers interested in classical gravity, quantum gravity and geometrical methods in field theory. It can also be recommended as a supplementary graduate textbook.

These lectures provide a systematic introduction to the physics/astrophysics and mathematics of black holes at a level suitable for graduate students, postdocs and researchers in physics, astrophysics, astronomy, and applied mathematics.

The present work covers practically all aspects of black hole physics and its astrophysical applications. Among the topics treated in depth are: space-time of stationary black holes, general theory of black holes, black hole perturbations, black hole numerics, black hole electrodynamics, black holes in unified theories of gravity, quantum black holes, final states of evaporating black holes and the information loss puzzle.Показать полностьюThe present work covers practically all aspects of black hole physics and its astrophysical applications. Among the topics treated in depth are: space-time of stationary black holes, general theory of black holes, black hole perturbations, black hole numerics, black hole electrodynamics, black holes in unified theories of gravity, quantum black holes, final states of evaporating black holes and the information loss puzzle. Special attention is paid to the role of black holes in astrophysics and observational evidence of black hole existence. Many exotic subjects linked with black holes, such as white holes, wormholes, and time machines are discussed in detail. Numerous appendices cover mathematical aspects of general relativity and black holes and quantum field theory in curved spacetime. This makes the book practically self-contained. Extensive references provide the reader with a guide to the literature in this field. Audience: This book will be of interest to researchers and postgraduate students whose work involves relativity and gravitation, statistical physics, thermo-dynamics, active galactic nuclei and stellar physics.

Cosmology for string theorists, a crash course

This review concerns the origin and the possible e!ects of magnetic "elds in the early Universe. We start by providing the reader with a short overview of the current state of the art of observations of cosmic magnetic "elds.Показать полностьюThis review concerns the origin and the possible e!ects of magnetic "elds in the early Universe. We start by providing the reader with a short overview of the current state of the art of observations of cosmic magnetic "elds. We then illustrate the arguments in favor of a primordial origin of magnetic "elds in the galaxies and in the clusters of galaxies. We argue that the most promising way to test this hypothesis is to look for possible imprints of magnetic "elds on the temperature and polarization anisotropies of the cosmic microwave background radiation (CMBR). With this purpose in mind,we provide a review of the most relevant e!ects of magnetic "elds on the CMBR. A long chapter of this review is dedicated to particle-physics-inspired models which predict the generation of magnetic "elds during the early Universe evolution. Although it is still unclear if any of these models can really explain the origin of galactic and intergalactic magnetic "elds,we show that interesting e!ects may arise anyhow. Among these e!ects,we discuss the consequences of strong magnetic "elds on the big-bang nucleosynthesis,on the masses and couplings of the matter constituents, on the electroweak phase transition,and on the baryon and lepton number violating sphaleron processes. Several intriguing common aspects,and possible interplay, of magnetogenesis and baryogenesis are also discussed.

This book definely matches a lot of students. Provides information about principles of Lecture notes on general relativity.

Stephen Hawking, the Lucasian Professor of Mathematics at Cambridge University, has made important theoretical contributions to gravitational theory and has played a major role in the development of cosmology and black hole physics.Показать полностьюStephen Hawking, the Lucasian Professor of Mathematics at Cambridge University, has made important theoretical contributions to gravitational theory and has played a major role in the development of cosmology and black hole physics. Hawking’s early work, partly in collaboration with Roger Penrose, showed the significance of spacetime singularities for the big bang and black holes. His later work has been concerned with a deeper understanding of these two issues. The work required extensive use of the two great intellectual achievements of the first half of the Twentieth Century: general relativity and quantum mechanics; and these are reflected in the reprinted articles. Hawking’s key contributions on black hole radiation and the no-boundary condition on the origin of the universe are included. The present compilation of Stephen Hawking’s most important work also includes an introduction by him, which guides the reader though the major highlights of the volume. This volume is thus an essential item in any library and will be an important reference source for those interested in theoretical physics and applied mathematics. It is an excellent thing to have so many of Professor Hawking’s most important contributions to the theory of black holes and space-time singularities all collected together in one handy volume. I am very glad to have them". Roger Penrose (Oxford) "This was an excellent idea to put the best papers by Stephen Hawking together. Even his papers written many years ago remain extremely useful for those who study classical and quantum gravity. By watching the evolution of his ideas one can get a very clear picture of the development of quantum cosmology during thelast quarter of this century". Andrei Linde (Stanford) "This review could have been quite short: 'The book contains a selection of 21 of Stephen Hawking’s most significant papers with an overview written by the author'. This would be sufficient to convince any researcher, student or librarian to acquire the book, so indisputable is the contribution of this man to the theoretical physics of the last half of our century ... Collected together, these brilliant works constitute a valuable contribution to the literature on modern classical and quantum gravity and cosmology. This book will certainly be a source of inspiration for new generations of physicists entering into this fascinating area of research". D Gal'tsov Classical & Quantum Gravity

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.Показать полностьюEinstein’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. These conditions are shown to be satisfied in the vicinity of stars of more than twice the solar mass near the endpoint of their nuclear evolution, and in a time-reversed sense for the universe as a whole. In the first case, the singularity in our past. A discussion of the Cauchy problem for General Relativity is also included in the book.

This book contains some of the papers of the world’s foremost researchers in cosmology, relativity and particle physics. Here in one volume, the reader can find out about the significant and exciting advances made in the physical sciences today. Contributors include Hawking, Israel, Penrose, Witten, Schwarz and others.

Who doesn't love a good argument? When physics heavyweights Stephen W. Hawking and Roger Penrose delivered three sets of back-and-forth lectures capped by a final debate at Cambridge’s Isaac Newton Institute, the course of modern cosmological thinking was at stake.Показать полностьюWho doesn't love a good argument? When physics heavyweights Stephen W. Hawking and Roger Penrose delivered three sets of back-and-forth lectures capped by a final debate at Cambridge’s Isaac Newton Institute, the course of modern cosmological thinking was at stake. As it happens, The Nature of Space and Time, which collects these remarks, suggests that little has changed from the days when Einstein challenged Bohr by refusing to believe that God plays dice. The math is more abstruse, the arguments more refined, but the argument still hinges on whether our physical theories should be expected to model reality or merely predict measurements.

In Einstein’s gravitational theory, the spacetime is Riemannian, that is, it has vanishing torsion and vanishing nonmetricity (covariant derivative of the metric).Показать полностьюIn Einstein’s gravitational theory, the spacetime is Riemannian, that is, it has vanishing torsion and vanishing nonmetricity (covariant derivative of the metric). In the gauging of the general affine group AD,R) and of its subgroup GLD, R) in four dimensions, energy-momentum and hypermomentum currents of matter are canonically coupled to the coframe and to the connection of a metric-affine spacetime with nonvanishing torsion and nonmetricity, respectively. Fermionic matter can be described in this framework by half-integer representations of the SLD, R) covering subgroup. We set up a (first-order) Lagrangian formalism and build up the corresponding Noether machinery. For an arbitrary gauge Lagrangian, the three gauge field equations come out in a suggestive Yang-Mills like form. The conservation-type differential identities for energy-momentum and hypermomentum and the corresponding complexes and superpotentials are derived. Limiting cases such as the Einstein-Cartan theory are discussed. In particular we show, how the AD,R) may “break down” to the Poincare (inhomogeneous Lorentz) group. In this context, we present explicit models for a symmetry breakdown in the cases of the Weyl (or homothetic) group, the SLD, R), or the GLD,R).