Advanced Lectures on General Relativity

Advanced Lectures on General Relativity
Author: Geoffrey Compère
Publisher: Springer
Total Pages: 148
Release: 2019-01-31
Genre: Science
ISBN: 303004260X

These lecture notes are intended for starting PhD students in theoretical physics who have a working knowledge of General Relativity. The four topics covered are: Surface charges as conserved quantities in theories of gravity; Classical and holographic features of three-dimensional Einstein gravity; Asymptotically flat spacetimes in four dimensions: BMS group and memory effects; The Kerr black hole: properties at extremality and quasi-normal mode ringing. Each topic starts with historical foundations and points to a few modern research directions.

Mathematical Problems of General Relativity I

Mathematical Problems of General Relativity I
Author: Demetrios Christodoulou
Publisher: European Mathematical Society
Total Pages: 164
Release: 2008
Genre: Science
ISBN: 9783037190050

General relativity is a theory proposed by Einstein in 1915 as a unified theory of space, time and gravitation. It is based on and extends Newton's theory of gravitation as well as Newton's equations of motion. It is thus fundamentally rooted in classical mechanics. The theory can be seen as a development of Riemannian geometry, itself an extension of Gauss' intrinsic theory of curved surfaces in Euclidean space. The domain of application of the theory is astronomical systems. One of the mathematical methods analyzed and exploited in the present volume is an extension of Noether's fundamental principle connecting symmetries to conserved quantities. This is involved at a most elementary level in the very definition of the notion of hyperbolicity for an Euler-Lagrange system of partial differential equations. Another method, the study and systematic use of foliations by characteristic (null) hypersurfaces, is in the spirit of Roger Penrose's approach in his incompleteness theorem. The methods have applications beyond general relativity to problems in fluid mechanics and, more generally, to the mechanics and electrodynamics of continuous media. The book is intended for advanced students and researchers seeking an introduction to the methods and applications of general relativity.

General Relativity

General Relativity
Author: Robert M. Wald
Publisher: University of Chicago Press
Total Pages: 507
Release: 2010-05-15
Genre: Science
ISBN: 0226870375

"Wald's book is clearly the first textbook on general relativity with a totally modern point of view; and it succeeds very well where others are only partially successful. The book includes full discussions of many problems of current interest which are not treated in any extant book, and all these matters are considered with perception and understanding."—S. Chandrasekhar "A tour de force: lucid, straightforward, mathematically rigorous, exacting in the analysis of the theory in its physical aspect."—L. P. Hughston, Times Higher Education Supplement "Truly excellent. . . . A sophisticated text of manageable size that will probably be read by every student of relativity, astrophysics, and field theory for years to come."—James W. York, Physics Today

Special Relativity, Electrodynamics, and General Relativity

Special Relativity, Electrodynamics, and General Relativity
Author: John B. Kogut
Publisher: Academic Press
Total Pages: 456
Release: 2018-01-09
Genre: Science
ISBN: 0128137215

Special Relativity, Electrodynamics, and General Relativity: From Newton to Einstein is intended to teach students of physics, astrophysics, astronomy, and cosmology how to think about special and general relativity in a fundamental but accessible way. Designed to render any reader a "master of relativity, all material on the subject is comprehensible and derivable from first principles. The book emphasizes problem solving, contains abundant problem sets, and is conveniently organized to meet the needs of both student and instructor. - Fully revised and expanded second edition with improved figures - Enlarged discussion of dynamics and the relativistic version of Newton's second law - Resolves the twin paradox from the principles of special and general relativity - Includes new chapters which derive magnetism from relativity and electrostatics - Derives Maxwell's equations from Gauss' law and the principles of special relativity - Includes new chapters on differential geometry, space-time curvature, and the field equations of general relativity - Introduces black holes and gravitational waves as illustrations of the principles of general relativity and relates them to the 2015 and 2017 observational discoveries of LIGO

Topics in the Foundations of General Relativity and Newtonian Gravitation Theory

Topics in the Foundations of General Relativity and Newtonian Gravitation Theory
Author: David B. Malament
Publisher: University of Chicago Press
Total Pages: 363
Release: 2012-04-02
Genre: Science
ISBN: 0226502473

In Topics in the Foundations of General Relativity and Newtonian Gravitation Theory, David B. Malament presents the basic logical-mathematical structure of general relativity and considers a number of special topics concerning the foundations of general relativity and its relation to Newtonian gravitation theory. These special topics include the geometrized formulation of Newtonian theory (also known as Newton-Cartan theory), the concept of rotation in general relativity, and Gödel spacetime. One of the highlights of the book is a no-go theorem that can be understood to show that there is no criterion of orbital rotation in general relativity that fully answers to our classical intuitions. Topics is intended for both students and researchers in mathematical physics and philosophy of science.

Spacetime and Geometry

Spacetime and Geometry
Author: Sean M. Carroll
Publisher: Cambridge University Press
Total Pages: 529
Release: 2019-08-08
Genre: Science
ISBN: 1108488390

An accessible introductory textbook on general relativity, covering the theory's foundations, mathematical formalism and major applications.

A First Course in General Relativity

A First Course in General Relativity
Author: Bernard Schutz
Publisher: Cambridge University Press
Total Pages: 411
Release: 2009-05-14
Genre: Science
ISBN: 0521887054

Second edition of a widely-used textbook providing the first step into general relativity for undergraduate students with minimal mathematical background.

3+1 Formalism in General Relativity

3+1 Formalism in General Relativity
Author: Éric Gourgoulhon
Publisher: Springer
Total Pages: 304
Release: 2012-02-27
Genre: Science
ISBN: 3642245250

This graduate-level, course-based text is devoted to the 3+1 formalism of general relativity, which also constitutes the theoretical foundations of numerical relativity. The book starts by establishing the mathematical background (differential geometry, hypersurfaces embedded in space-time, foliation of space-time by a family of space-like hypersurfaces), and then turns to the 3+1 decomposition of the Einstein equations, giving rise to the Cauchy problem with constraints, which constitutes the core of 3+1 formalism. The ADM Hamiltonian formulation of general relativity is also introduced at this stage. Finally, the decomposition of the matter and electromagnetic field equations is presented, focusing on the astrophysically relevant cases of a perfect fluid and a perfect conductor (ideal magnetohydrodynamics). The second part of the book introduces more advanced topics: the conformal transformation of the 3-metric on each hypersurface and the corresponding rewriting of the 3+1 Einstein equations, the Isenberg-Wilson-Mathews approximation to general relativity, global quantities associated with asymptotic flatness (ADM mass, linear and angular momentum) and with symmetries (Komar mass and angular momentum). In the last part, the initial data problem is studied, the choice of spacetime coordinates within the 3+1 framework is discussed and various schemes for the time integration of the 3+1 Einstein equations are reviewed. The prerequisites are those of a basic general relativity course with calculations and derivations presented in detail, making this text complete and self-contained. Numerical techniques are not covered in this book.

Advanced General Relativity

Advanced General Relativity
Author: John Stewart
Publisher: Cambridge University Press
Total Pages: 244
Release: 1993-11-26
Genre: Science
ISBN: 9780521449465

A self-contained introduction to advanced general relativity.

Lectures on General Relativity, Cosmology and Quantum Black Holes

Lectures on General Relativity, Cosmology and Quantum Black Holes
Author: Badis Ydri
Publisher:
Total Pages: 0
Release: 2017
Genre: Cosmology
ISBN: 9780750314770

"This book is a rigorous text for students in physics and mathematics requiring an introduction to the implications and interpretation of general relativity in areas of cosmology. Readers of this text will be well prepared to follow the theoretical developments in the field and undertake research projects as part of an MSc or PhD programme. This ebook contains interactive Q & A technology, allowing the reader to interact with the text and reveal answers to selected exercises posed by the author within the book. This feature may not function in all formats and on reading devices."--Prové de l'editor.