The Geometry of Kerr Black Holes

Author: Barrett O'Neill
Publisher: Courier Corporation
ISBN: 0486783111
Format: PDF, ePub
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Suitable for advanced undergraduates and graduate students of mathematics as well as for physicists, this unique monograph and self-contained treatment constitutes an introduction to modern techniques in differential geometry. 1995 edition.

The Mathematical Theory of Black Holes

Author: Subrahmanyan Chandrasekhar
Publisher: Oxford University Press
ISBN: 9780198503705
Format: PDF, Mobi
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"The theory of black holes is the most simple consequence of Einstein's relativity theory. Dealing with relativity theory, this book details one of the most beautiful areas of mathematical physics; the theory of black holes. It represents a personal testament to the work of the author, who spent several years working-out the subject matter." --WorldCat.

Curvature in Mathematics and Physics

Author: Shlomo Sternberg
Publisher: Courier Corporation
ISBN: 0486292711
Format: PDF, ePub, Mobi
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Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.

General Relativity

Author: Norbert Straumann
Publisher: Springer Science & Business Media
ISBN: 3662118270
Format: PDF, ePub
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The foundations are thoroughly developed together with the required mathematical background from differential geometry developed in Part III. The author also discusses the tests of general relativity in detail, including binary pulsars, with much space is devoted to the study of compact objects, especially to neutron stars and to the basic laws of black-hole physics. This well-structured text and reference enables readers to easily navigate through the various sections as best matches their backgrounds and perspectives, whether mathematical, physical or astronomical. Very applications oriented, the text includes very recent results, such as the supermassive black-hole in our galaxy and first double pulsar system

Semi Riemannian Geometry With Applications to Relativity

Author: Barrett O'Neill
Publisher: Academic Press
ISBN: 9780080570570
Format: PDF, ePub, Mobi
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This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest.

Introduction to Black Hole Physics

Author: Valeri P. Frolov
Publisher: Oxford University Press
ISBN: 0199692297
Format: PDF, ePub
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What is a black hole? How many of them are in our Universe? Can black holes be created in a laboratory or in particle colliders? Can objects similar to black holes be used for space and time travel? This book discusses these and many other questions providing the reader with the tools required to explore the Black Hole Land independently.

Physical Foundations of Cosmology

Author: Viatcheslav Mukhanov
Publisher: Cambridge University Press
ISBN: 1139447114
Format: PDF
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Inflationary cosmology has been developed over the last twenty years to remedy serious shortcomings in the standard hot big bang model of the universe. This textbook, first published in 2005, explains the basis of modern cosmology and shows where the theoretical results come from. The book is divided into two parts; the first deals with the homogeneous and isotropic model of the Universe, the second part discusses how inhomogeneities can explain its structure. Established material such as the inflation and quantum cosmological perturbation are presented in great detail, however the reader is brought to the frontiers of current cosmological research by the discussion of more speculative ideas. An ideal textbook for both advanced students of physics and astrophysics, all of the necessary background material is included in every chapter and no prior knowledge of general relativity and quantum field theory is assumed.

Renormalization

Author: John C. Collins
Publisher: Cambridge University Press
ISBN: 9780521311779
Format: PDF, ePub, Mobi
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This book provides a coherent exposition of the techniques underlying these calculations.

Black Holes Thermodynamics Information and Firewalls

Author: Robert B. Mann
Publisher: Springer
ISBN: 3319144960
Format: PDF, Kindle
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This book reflects the resurgence of interest in the quantum properties of black holes, culminating most recently in controversial discussions about firewalls. On the thermodynamic side, it describes how new developments allowed the inclusion of pressure/volume terms in the first law, leading to a new understanding of black holes as chemical systems, experiencing novel phenomena such as triple points and reentrant phase transitions. On the quantum-information side, the reader learns how basic arguments undergirding quantum complementarity have been shown to be flawed; and how this suggests that a black hole may surround itself with a firewall: a violent and chaotic region of highly excited states. In this thorough and pedagogical treatment, Robert Mann traces these new developments from their roots to our present-day understanding, highlighting their relationships and the challenges they present for quantum gravity.

Elementary Differential Geometry

Author: Barrett O'Neill
Publisher: Academic Press
ISBN: 148326811X
Format: PDF
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Elementary Differential Geometry focuses on the elementary account of the geometry of curves and surfaces. The book first offers information on calculus on Euclidean space and frame fields. Topics include structural equations, connection forms, frame fields, covariant derivatives, Frenet formulas, curves, mappings, tangent vectors, and differential forms. The publication then examines Euclidean geometry and calculus on a surface. Discussions focus on topological properties of surfaces, differential forms on a surface, integration of forms, differentiable functions and tangent vectors, congruence of curves, derivative map of an isometry, and Euclidean geometry. The manuscript takes a look at shape operators, geometry of surfaces in E, and Riemannian geometry. Concerns include geometric surfaces, covariant derivative, curvature and conjugate points, Gauss-Bonnet theorem, fundamental equations, global theorems, isometries and local isometries, orthogonal coordinates, and integration and orientation. The text is a valuable reference for students interested in elementary differential geometry.