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Book
Introduction to general relativity, black holes, and cosmology
Authors: ---
ISBN: 9780199666454 0199666458 9780199666461 0199666466 0191644528 9780191644528 0191644536 0191936502 Year: 2023 Publisher: Oxford : Oxford University Press,

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Abstract

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 large scale structure of space-time
Authors: ---
ISBN: 0521200164 9780521200165 0521099064 9780521099066 9780511524646 1139811223 113981169X 0511524641 1139811444 0511935145 1283870762 1139811568 9781107188792 1139635638 1107188792 9781139811699 9781139635639 9781139811224 9781139811446 9780511935145 9781283870764 9781139811569 Year: 1974 Publisher: Cambridge 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.

Relativity: an introduction to special and general relativity
Author:
ISBN: 0521811856 0521010691 9780521811859 9780511616532 9780521010696 9780511648090 051164809X 110714437X 0511187203 0511561571 0511616538 0511186274 Year: 2004 Publisher: Cambridge Cambridge University Press

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Thoroughly revised and updated, this textbook provides a pedagogical introduction to relativity. It is self-contained, but the reader is expected to have a basic knowledge of theoretical mechanics and electrodynamics. It covers the most important features of both special and general relativity, as well as touching on more difficult topics, such as the field of charged pole-dipole particles, the Petrov classification, groups of motions, gravitational lenses, exact solutions and the structure of infinity. The necessary mathematical tools (tensor calculus, Riemannian geometry) are provided, most of the derivations are given in full, and exercises are included where appropriate. Written as a textbook for undergraduate and introductory graduate courses, it will also be of use to researchers working in the field. The bibliography gives the original papers and directs the reader to useful monographs and review papers.

Exact solutions of Einstein's field equations
Authors: --- ---
ISBN: 1107126614 1280414669 9786610414666 0511178743 1139145509 0511065485 0511059175 0511305931 051153518X 0511067615 9780511065484 9780511067617 9780511535185 9780521461368 0521461367 9780521467025 0521467020 9780521467025 9781107126619 9781280414664 6610414661 9780511178740 9781139145503 9780511059179 9780511305931 Year: 2003 Publisher: Cambridge Cambridge University press

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A paperback edition of a classic text, this book gives a unique survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources. It introduces the foundations of differential geometry and Riemannian geometry and the methods used to characterize, find or construct solutions. The solutions are then considered, ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties. Includes all the developments in the field since the first edition and contains six completely new chapters, covering topics including generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics. It can also be used as an introductory text on some mathematical aspects of general relativity.

Classical geometries in modern contexts : geometry of real inner product spaces
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ISBN: 3764373717 3764374322 9783764373719 9786610460083 1280460083 Year: 2005 Publisher: Basel ; Boston : Birkhauser Verlag,

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This book is based on real inner product spaces X of arbitrary (finite or infinite) dimension greater than or equal to 2. With natural properties of (general) translations and general distances of X, euclidean and hyperbolic geometries are characterized. For these spaces X also the sphere geometries of Möbius and Lie are studied (besides euclidean and hyperbolic geometry), as well as geometries where Lorentz transformations play the key role. The geometrical notions of this book are based on general spaces X as described. This implies that also mathematicians who have not so far been especially interested in geometry may study and understand great ideas of classical geometries in modern and general contexts. Proofs of newer theorems, characterizing isometries and Lorentz transformations under mild hypotheses are included, like for instance infinite dimensional versions of famous theorems of A.D. Alexandrov on Lorentz transformations. A real benefit is the dimension-free approach to important geometrical theories. Only prerequisites are basic linear algebra and basic 2- and 3-dimensional real geometry.

Special and General Relativity : With Applications to White Dwarfs, Neutron Stars and Black Holes
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ISBN: 9780387471099 0387471065 9780387471068 038747109X 1441923667 Year: 2007 Publisher: New York, NY : Springer New York : Imprint: Springer,

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Special and General Relativity are concisely developed together with essential aspects of nuclear and particle physics. Problem sets are provided for many chapters, making the book ideal for a course on the physics of white dwarf and neutron star interiors.

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