487,20 zł

Exact Space-Times in Einstein's General Relativity Cambridge University Press

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Einstein's theory of general relativity is a theory of gravity and, as in the earlier Newtonian theory, much can be learnt about the character of gravitation and its effects by investigating particular idealised examples. This book, first published in 2009, describes the basic solutions of Einstein's equations with a particular emphasis on what they mean, both geometrically and physically. Concepts such as big bang and big crunch-types of singularities, different kinds of horizons and gravitational waves, are described in the context of the particular space-times in which they naturally arise. These notions are initially introduced using the most simple and symmetric cases. Various important coordinate forms of each solution are presented, thus enabling the global structure of the corresponding space-time and its other properties to be analysed. The book is an invaluable resource both for graduate students and academic researchers working in gravitational physics.

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259,77 zł

Introduction to General Relativity, Black Holes, and Cosmology Oxford University Press

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General Relativity is a beautiful geometric theory, simple in its mathematical formulation but leading to numerous consequences with striking physical interpretations: gravitational waves, black holes, cosmological models, and so on. This introductory textbook is written for mathematics students interested in physics and physics students interested in exact mathematical formulations (or for anyone with a scientific mind who is curious to know more of the world we live in), recent remarkable experimental and observational results which confirm the theory are clearly described and no specialised physics knowledge is required. The mathematical level of Part A is aimed at undergraduate students and could be the basis for a course on General Relativity. Part B is more advanced, but still does not require sophisticated mathematics. Based on Yvonne Choquet-Bruhat's more advanced text, General Relativity and the Einstein Equations, the aim of this book is to give with precision, but as simply as possible, the foundations and main consequences of General Relativity.The first five chapters from General Relativity and the Einstein Equations have been updated with new sections and chapters on black holes, gravitational waves, singularities, and the Reissner-Nordstrom and interior Schwarzchild solutions. The rigour behind this book will provide readers with the perfect preparation to follow the great mathematical progress in the actual development, as well as the ability to model, the latest astrophysical and cosmological observations. The book presents basic General Relativity and provides a basis for understanding and using the fundamental theory.

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467,90 zł

General Relativity Cambridge University Press

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General Relativity: An Introduction for Physicists provides a clear mathematical introduction to Einstein's theory of general relativity. It presents a wide range of applications of the theory, concentrating on its physical consequences. After reviewing the basic concepts, the authors present a clear and intuitive discussion of the mathematical background, including the necessary tools of tensor calculus and differential geometry. These tools are then used to develop the topic of special relativity and to discuss electromagnetism in Minkowski spacetime. Gravitation as spacetime curvature is then introduced and the field equations of general relativity derived. After applying the theory to a wide range of physical situations, the book concludes with a brief discussion of classical field theory and the derivation of general relativity from a variational principle. Written for advanced undergraduate and graduate students, this approachable textbook contains over 300 exercises to illuminate and extend the discussion in the text.

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178,57 zł

General Theory of Relativity Princeton University Press

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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. 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 Relativity" comprises thirty-five compact chapters that take the reader point-by-point through the necessary steps for understanding general relativity.

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88,83 zł

Relativity Ancient Wisdom Publications

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General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1915. It is the current description of gravitation in modern physics. General relativity generalises special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the four-momentum (mass-energy and linear momentum) of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations. Einstein's theory has important astrophysical implications. For example, it implies the existence of black holes-regions of space in which space and time are distorted in such a way that nothing, not even light, can escape-as an end-state for massive stars. There is evidence that such stellar black holes as well as more massive varieties of black hole are responsible for the intense radiation emitted by certain types of astronomical objects such as active galactic nuclei or microquasars.

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73,25 zł

Introduction to Tensor Calculus, Relativity and Cosmology Dover Publications Inc.

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PrefaceList of ConstantsChapter 1 Special Principle of Relativity. Lorentz Transformations1. Newton's laws of motion2. Covariance of the laws of motion3. Special principle of relativity4. Lorentz transformations. Minkowski space-time5. The special Lorentz transformation6. Fitzgerald contraction. Time dilation7. Spacelike and timelike intervals. Light cone Exercises 1Chapter 2 Orthogonal Transformations. Cartesian Tensors8. Orthogonal transformations9. Repeated-index summation convention10. Rectangular Cartesian tensors11. Invariants. Gradients. Derivatives of tensors12. Contraction. Scalar product. Divergence13. Pseudotensors14. Vector products. Curl Exercises 2Chapter 3 Special Relativity Mechanics15. The velocity vector16. Mass and momentum17. The force vector. Energy18. Lorentz transformation equations for force19. Fundamental particles. Photon and neutrino20. Lagrange's and Hamilton's equations21. Energy-momentum tensor22. Energy-momentum tensor for a fluid23. Angular momentum Exercises 3Chapter 4 Special Relativity Electrodynamics24. 4-Current density25. 4-Vector potential26. The field tensor27. Lorentz transformations of electric and magnetic vectors28. The Lorentz force29. The engery-momentum tensor for an electromagnetic field Exercises 4Chapter 5 General Tensor Calculus. Riemannian Space30. Generalized N-dimensional spaces31. Contravariant and covariant tensors32. The quotient theorem. Conjugate tensors33. Covariant derivatives. Parallel displacement. Affine connection34. Transformation of an affinity35. Covariant derivatives of tensors36. The Riemann-Christoffel curvature tensor37. Metrical connection. Raising and lowering indices38. Scalar products. Magnitudes of vectors39. Geodesic frame. Christoffel symbols40. Bianchi identity41. The covariant curvature tensor42. Divergence. The Laplacian. Einstein's tensor43. Geodesics Exercises 5Chapter 6 General Theory of Relativity44. Principle of equivalence45. Metric in a gravitational field46. Motion of a free particle in a gravitational field47. Einstein's law of gravitation48. Acceleration of a particle in a weak gravitational field49. Newton's law of gravitation50. Freely falling dust cloud51. Metrics with spherical symmetry52. Schwarzchild's solution53. Planetary orbits54. Gravitational deflection of a light ray55. Gravitational displacement of spectral lines56. Maxwell's equations in a gravitational field57. Black holes58. Gravitational waves Exercises 6Chapter 7 Cosmology59. Cosmological principle. Cosmical time60. Spaces of constant curvature61. The Robertson-Walker metric62. Hubble's constant and the deceleration parameter63. Red shifts of galaxies64. Luminosity distance65. Cosmic dynamics66. Model universes of Einstein and de Sitter67. Friedmann universes68. Radiation model69. Particle and event horizons Exercises 7ReferencesBibliographyIndex

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42,60 zł

Introducing Relativity Icon Books

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It is now more than a century since Einstein's theories of Special and General Relativity began to revolutionise our view of the universe. Beginning near the speed of light and proceeding to explorations of space-time and curved spaces, "Introducing Relativity" plots a visually accessible course through the thought experiments that have given shape to contemporary physics. Scientists from Newton to Hawking add their unique contributions to this story, as we encounter Einstein's astounding vision of gravity as the curvature of space-time and arrive at the breathtakingly beautiful field equations. Einstein's legacy is reviewed in the most advanced frontiers of physics today - black holes, gravitational waves, the accelerating universe and string theory. This is a superlative, fascinating graphic account of Einstein's strange world and how his legacy has been built upon since.

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285,30 zł

Introduction to Mathematical Relativity Springer Nature Switzerland AG

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This concise textbook introduces the reader to advanced mathematical aspects of general relativity, covering topics like Penrose diagrams, causality theory, singularity theorems, the Cauchy problem for the Einstein equations, the positive mass theorem, and the laws of black hole thermodynamics. It emerged from lecture notes originally conceived for a one-semester course in Mathematical Relativity which has been taught at the Instituto Superior Técnico (University of Lisbon, Portugal) since 2010 to Masters and Doctorate students in Mathematics and Physics. Mostly self-contained, and mathematically rigorous, this book can be appealing to graduate students in Mathematics or Physics seeking specialization in general relativity, geometry or partial differential equations. Prerequisites include proficiency in differential geometry and the basic principles of relativity. Readers who are familiar with special relativity and have taken a course either in Riemannian geometry (for students of Mathematics) or in general relativity (for those in Physics) can benefit from this book.

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201,08 zł

Large Scale Structure of Space-Time Cambridge University Press

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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.

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732,61 zł

Mathematical Aspects of Paradoxes in Cosmology Springer, Berlin

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This book provides a mathematical and numerical analysis of many problems which lead to paradoxes in contemporary cosmology, in particular, the existence of dark matter and dark energy. It is shown that these hypothetical quantities arise from excessive extrapolations of simple mathematical models to the whole physical universe. Written in a completely different style to most books on General Relativity and cosmology, the important results take the form of mathematical theorems with precise assumptions and statements. All theorems are followed by a corresponding proof, or an exact reference to the proof.Some nonstandard topics are also covered, including violation of the causality principle in Newtonian mechanics, a critical mathematical and numerical analysis of Mercury's perihelion shift, inapplicability of Einstein's equations to the classical two-body problem due to computational complexity, non-uniqueness of the notion of universe, the topology of the universe, various descriptions of a hypersphere, regular tessellations of hyperbolic spaces, local Hubble expansion of the universe, neglected gravitational redshift in the detection of gravitational waves, and the possible distribution of mass inside a black hole. The book also dispels some myths appearing in the theory of relativity and in contemporary cosmology. For example, although the hidden assumption that Einstein's equations provide a good description of the evolution of the whole universe is considered to be obvious, it is just a null hypothesis which has not been verified by any experiment, and has only been postulated by excessive extrapolations of many orders of magnitude.

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475,74 zł

Gravity Cambridge University Press

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Exploring approximate solutions to general relativity and their consequences, this textbook offers a unique presentation of Einstein's theory by developing powerful methods that can be applied to astrophysical systems. Beginning with a uniquely thorough treatment of Newtonian gravity, the book develops post-Newtonian and post-Minkowskian approximation methods to obtain weak-field solutions to the Einstein field equations. It explores the motion of self-gravitating bodies, the physics of gravitational waves, and the impact of radiative losses on gravitating systems. The book concludes with a brief overview of alternative theories of gravity. Ideal for graduate courses on general relativity and relativistic astrophysics, the book examines real-life applications, such as planetary motion around the Sun, the timing of binary pulsars, and gravitational waves emitted by binary black holes. Text boxes explore related topics and provide historical context, and over 100 exercises present interesting and challenging tests of the material covered in the main text.

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1018,12 zł

Gravity, a Geometrical Course Springer

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Gravity, a Geometrical Course presents general relativity (GR) in a systematic and exhaustive way, covering three aspects that are homogenized into a single texture: i) the mathematical, geometrical foundations, exposed in a self consistent contemporary formalism, ii) the main physical, astrophysical and cosmological applications, updated to the issues of contemporary research and observations, with glimpses on supergravity and superstring theory, iii) the historical development of scientific ideas underlying both the birth of general relativity and its subsequent evolution. The book, divided in two volumes, is a rich resource for graduate students and those who wish to gain a deep knowledge of the subject without an instructor. §Volume One is dedicated to the development of the theory and basic physical applications. It guides the reader from the foundation of special relativity to Einstein field equations, illustrating some basic applications in astrophysics. A detailed account of the historical and conceptual development of the theory is combined with the presentation of its mathematical foundations. Differentiable manifolds, fibre-bundles, differential forms, and the theory of connections are covered, with a sketchy introduction to homology and cohomology. (Pseudo)-Riemannian geometry is presented both in the metric and in the vielbein approach. Physical applications include the motions in a Schwarzschild field leading to the classical tests of GR (light-ray bending and periastron advance) discussion of relativistic stellar equilibrium, white dwarfs, Chandrasekhar mass limit and polytropes. An entire chapter is devoted to tests of GR and to the indirect evidence of gravitational wave emission. The formal structure of gravitational theory is at all stages compared with that of non gravitational gauge theories, as a preparation to its modern extension, namely supergravity, discussed in the second volume. §Pietro Fr

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220,58 zł

Introduction To Differential Geometry - With The Use Of Tensor Calculus Read Books

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AN INTRODUCTION TO DIFFERENTIAL GEOMETRY WITH USE OF THE TENSOR CALCULUS By LUTHER PFAHLER EISENHART. Preface: Since 1909, when my Differential Geometry of Curves and Surfaces was published, the tensor calculus, which had previously been invented by Ricci, was adopted by Einstein in his General Theory of Relativity, and has been developed further in the study of Riemannian Geometry and various generalizations of the latter. In the present book the tensor calculus of cuclidean 3-space is developed and then generalized so as to apply to a Riemannian space of any number of dimensions. The tensor calculus as here developed is applied in Chapters III and IV to the study of differential geometry of surfaces in 3-space, the material treated being equivalent to what appears in general in the first eight chapters of my former book with such additions as follow from the introduction of the concept of parallelism of Levi-Civita and the content of the tensor calculus. LUTHER PFAHLER EISENHART. Contents include: CHAPTER I CURVES IN SPACE SECTION PAGE 1. Curves ami surfaces. The summation convention 1 2. Length of a curve. Linear element , 8 3. Tangent to a curve. Order of contact. Osculating plane 11 4. Curvature. Principal normal. Circle of curvature 16 5. TBi normal. Torsion 19 6r The Frenet Formulas. The form of a curve in the neighborhood of a point 25 7. Intrinsic equations of a curve 31 8. Involutes and evolutes of a curve 34 9. The tangent surface of a curve. The polar surface. Osculating sphere. . 38 10. Parametric equations of a surface. Coordinates and coordinate curves trT a surface 44 11. 1 Tangent plane to a surface 50 tSffDovelopable surfaces. Envelope of a one-parameter family of surfaces. . 53 CHAPTER II TRANSFORMATION OF COORDINATES. TENSOR CALCULUS 13. Transformation of coordinates. Curvilinear coordinates 63 14. The fundamental quadratic form of space 70 15. Contravariant vectors. Scalars 74 16. Length of a contravariant vector. Angle between two vectors 80 17. Covariant vectors. Contravariant and covariant components of a vector 83 18. Tensors. Symmetric and skew symmetric tensors 89 19. Addition, subtraction and multiplication of tensors. Contraction.... 94 20. The Christoffel symbols. The Riemann tensor 98 21. The Frenet formulas in general coordinates 103 22. Covariant differentiation 107 23. Systems of partial differential equations of the first order. Mixed systems 114 CHAPTER III INTRINSIC GEOMETRY OF A SURFACE 24. Linear element of a surface. First fundamental quadratic form of a surface. Vectors in a surface 123 25. Angle of two intersecting curves in a surface. Element of area 129 26. Families of curves in a surface. Principal directions 138 27. The intrinsic geometry of a surface. Isometric surfaces 146 28. The Christoffel symbols for a surface. The Riemannian curvature tensor. The Gaussian curvature of a surface 149 29. Differential parameters 155 30. Isometric orthogonal nets. Isometric coordinates 161 31...

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385,29 zł

Gauge Fields, Knots And Gravity World Scientific Publishing Co Pte Ltd

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This is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity. The book begins with a rapid course on manifolds and differential forms, emphasizing how these provide a proper language for formulating Maxwell's equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvature in order to generalize Maxwell theory to the Yang-Mills equations. The relation of gauge theory to the newly discovered knot invariants such as the Jones polynomial is sketched. Riemannian geometry is then introduced in order to describe Einstein's equations of general relativity and show how an attempt to quantize gravity leads to interesting applications of knot theory.

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629,20 zł

Classical Field Theory Springer-Verlag Berlin and Heidelberg GmbH & Co....

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Scheck's successful textbook presents a comprehensive treatment, ideally suited for a one-semester course. The textbook describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams.Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes with a discussion of the Schwarzschild solution of Einstein's equations and the classical tests of general relativity.The new concept of this edition presents the content divided into two tracks: the fast track for master students, providing the essentials, and the intensive track for all wanting to get in depth knowledge of the field.Cleary labelled material and sections guide students through the preferred level of treatment.Numerous problems and worked examples will provide successful access to Classical Field Theory.

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