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This book combines relativity, astrophysics, and cosmology in a single volume, providing an introduction to each subject that enables students to understand more detailed treatises as well as the current literature. The section on general relativity gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes, Penrose processes, and similar topics), and considers the energy-momentum tensor for various solutions. The next section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects. Lastly, the section on cosmology discusses various cosmological models, observational tests, and scenarios for the early universe. * Clearly combines relativity, astrophysics, and cosmology in a single volume so students can understand more detailed treatises and current literature * Extensive introductions to each section are followed by relevant examples and numerous exercises * Provides an easy-to-understand approach to this advanced field of mathematics and modern physics by providing highly detailed derivations of all equations and results

Author : Derek F. Lawden
ISBN : 0486132145
Genre : Science
File Size : 82.90 MB
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This elementary introduction pays special attention to aspects of tensor calculus and relativity that students tend to find most difficult. Its use of relatively unsophisticated mathematics in the early chapters allows readers to develop their confidence within the framework of Cartesian coordinates before undertaking the theory of tensors in curved spaces and its application to general relativity theory. Topics include the special principle of relativity and Lorentz transformations; orthogonal transformations and Cartesian tensors; special relativity mechanics and electrodynamics; general tensor calculus and Riemannian space; and the general theory of relativity, including a focus on black holes and gravitational waves. The text concludes with a chapter offering a sound background in applying the principles of general relativity to cosmology. Numerous exercises advance the theoretical developments of the main text, thus enhancing this volume’s appeal to students of applied mathematics and physics at both undergraduate and postgraduate levels. Preface. List of Constants. References. Bibliography.

Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in motion, relativistic addition of velocities, and the twin paradox, as well as new material on gravitational waves, amongst other topics. Clearly combines relativity, astrophysics, and cosmology in a single volume Extensive introductions to each section are followed by relevant examples and numerous exercises Presents topics of interest to those researching and studying tensor calculus, the theory of relativity, gravitation, cosmology, quantum cosmology, Robertson-Walker Metrics, curvature tensors, kinematics, black holes, and more Fully revised and updated with 80 pages of new material on relativistic effects, such as relativity of simultaneity and relativity of the concept of distance, amongst other topics Provides an easy-to-understand approach to this advanced field of mathematics and modern physics by providing highly detailed derivations of all equations and results

Author : Eric A. Lord
ISBN : UOM:39015017212971
Genre : General relativity (Physics).
File Size : 89.77 MB
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The general theory of relativity and its applications to cosmology requires very deep understanding of mathematics and physics. Keeping this in mind, this self-contained textbook is written which addresses to general relativity and cosmology. In this book, the attempts have been made to explain mathematicians’ notions in the language of a physicist. Primarily intended for the postgraduate students of mathematics and physics, it gives equal importance to mathematical and physical aspects, and thus sharpens understanding of the theory. The text covers many modern concepts and current developments in gravity and cosmology including Brans-Dicke theory, higher-derivative gravity, Kaluza-Klein theory with extension to higher-dimensions. Besides PG students this book would also be useful for research scholars. KEY FEATURES Highlights special features of general relativity and cosmology. Discusses structure formation in the universe, inflationary models and dark energy models with special focus on basic concepts. Provides problems at the end of each chapter to stimulate thinking. Reveals interconnections between required mathematical concepts. Explains “how to apply mathematical concepts to physical problems”. Discusses lagrangian formulation of the field theory and action principle as it provides a powerful tool to derive field equations and energy-momentum tensor components.

Author : Jerzy Plebanski
ISBN : 9781139458405
Genre : Science
File Size : 38.59 MB
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General relativity is a cornerstone of modern physics, and is of major importance in its applications to cosmology. Plebanski and Krasinski are experts in the field and in this book they provide a thorough introduction to general relativity, guiding the reader through complete derivations of the most important results. Providing coverage from a unique viewpoint, geometrical, physical and astrophysical properties of inhomogeneous cosmological models are all systematically and clearly presented, allowing the reader to follow and verify all derivations. For advanced undergraduates and graduates in physics and astronomy, this textbook will enable students to develop expertise in the mathematical techniques necessary to study general relativity.

Author : Marcelo Samuel Berman
ISBN : 1600210139
Genre : Mathematics
File Size : 29.28 MB
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This book offers an introduction to General Relativity and its mathematical tools, together with an introduction to relativistic and scalar-tensor cosmologies. Part I deals with Tensor Calculus. Part II introduces General Relativity Theory, while Part III deals with Relativistic Cosmology. In Part IV we work Scalar-Tensor theories, concentrating in Cosmological Models. In the last chapters, the cosmological models presented, become more and more sophisticated, including some new cases, never published elsewhere, in which all fundamental "constants" are made to vary, with the age of the Universe, namely, the gravitational, the cosmological, the coupling Brans-Dicke "constants", the speed of light, Planck's "fine -structure "constant" alpha" etc. This is a mathematical cosmology textbook that may lead undergraduates, and graduate students, to one of the frontiers of research, while keeping the prerequisites to a minimum, because most of the theory in the book requires only prior knowledge of Calculus and a University Physics course.

Author : Christian G BÃ¶hmer
ISBN : 9781786341204
Genre : Science
File Size : 57.16 MB
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Introduction to General Relativity and Cosmology gives undergraduate students an overview of the fundamental ideas behind the geometric theory of gravitation and spacetime. Through pointers on how to modify and generalise Einstein's theory to enhance understanding, it provides a link between standard textbook content and current research in the field. Chapters present complicated material practically and concisely, initially dealing with the mathematical foundations of the theory of relativity, in particular differential geometry. This is followed by a discussion of the Einstein field equations and their various properties. Also given is analysis of the important Schwarzschild solutions, followed by application of general relativity to cosmology. Questions with fully worked answers are provided at the end of each chapter to aid comprehension and guide learning. This pared down textbook is specifically designed for new students looking for a workable, simple presentation of some of the key theories in modern physics and mathematics. Request Inspection Copy

Author : Valerio Faraoni
ISBN : 1402019882
Genre : Science
File Size : 80.26 MB
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Cosmology in Scalar-Tensor Gravity covers all aspects of cosmology in scalar-tensor theories of gravity. Considerable progress has been made in this exciting area of physics and this book is the first to provide a critical overview of the research. Among the topics treated are: -Scalar-tensor gravity and its limit to general relativity, -Effective energy-momentum tensors and conformal frames, -Gravitational waves in scalar-tensor cosmology, -Specific scalar-tensor theories, -Exact cosmological solutions and cosmological perturbations, -Scalar-tensor scenarios of the early universe and inflation, -Scalar-tensor models of quintessence in the present universe and their far-reaching consequences for the ultimate fate of the cosmos.

This book introduces the general theory of relativity and includes applications to cosmology. The book provides a thorough introduction to tensor calculus and curved manifolds. After the necessary mathematical tools are introduced, the authors offer a thorough presentation of the theory of relativity. Also included are some advanced topics not previously covered by textbooks, including Kaluza-Klein theory, Israel's formalism and branes. Anisotropic cosmological models are also included. The book contains a large number of new exercises and examples, each with separate headings. The reader will benefit from an updated introduction to general relativity including the most recent developments in cosmology.