Mathematics of Gravitation: Lorentzian geometry and Einstein equations
Author:
Publisher:
Published: 1997
Total Pages: 256
ISBN-13:
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General Relativity Without Calculus
Author: Jose Natario
Publisher: Springer Science & Business Media
Published: 2011-07-30
Total Pages: 133
ISBN-13: 3642214525
DOWNLOAD EBOOK“General Relativity Without Calculus” offers a compact but mathematically correct introduction to the general theory of relativity, assuming only a basic knowledge of high school mathematics and physics. Targeted at first year undergraduates (and advanced high school students) who wish to learn Einstein’s theory beyond popular science accounts, it covers the basics of special relativity, Minkowski space-time, non-Euclidean geometry, Newtonian gravity, the Schwarzschild solution, black holes and cosmology. The quick-paced style is balanced by over 75 exercises (including full solutions), allowing readers to test and consolidate their understanding.
Beyond Einstein
Author: David E. Rowe
Publisher: Birkhäuser
Published: 2018-06-18
Total Pages: 500
ISBN-13: 1493977083
DOWNLOAD EBOOKBeyond Einstein: Perspectives on Geometry, Gravitation, and Cosmology explores the rich interplay between mathematical and physical ideas by studying the interactions of major actors and the roles of important research communities over the course of the last century.
The Einstein Equations and the Large Scale Behavior of Gravitational Fields
Author: Piotr T. Chrusciel
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 487
ISBN-13: 3034879539
DOWNLOAD EBOOKThe book presents state-of-the-art results on the analysis of the Einstein equations and the large scale structure of their solutions. It combines in a unique way introductory chapters and surveys of various aspects of the analysis of the Einstein equations in the large. It discusses applications of the Einstein equations in geometrical studies and the physical interpretation of their solutions. Open problems concerning analytical and numerical aspects of the Einstein equations are pointed out. Background material on techniques in PDE theory, differential geometry, and causal theory is provided.
Einstein Equations: Physical and Mathematical Aspects of General Relativity
Author: Sergio Cacciatori
Publisher: Springer Nature
Published: 2019-11-23
Total Pages: 359
ISBN-13: 3030180611
DOWNLOAD EBOOKThis book is based on lectures given at the first edition of the Domoschool, the International Alpine School in Mathematics and Physics, held in Domodossola, Italy, in July 2018. It is divided into two parts. Part I consists of four sets of lecture notes. These are extended versions of lectures given at the Domoschool, written by well-known experts in mathematics and physics related to General Relativity. Part II collects talks by selected participants, focusing on research related to General Relativity.
Gravitational Curvature
Author: Theodore Frankel
Publisher: Courier Corporation
Published: 2013-04-10
Total Pages: 194
ISBN-13: 048628915X
DOWNLOAD EBOOKThis classic text and reference monograph applies modern differential geometry to general relativity. A brief mathematical introduction to gravitational curvature, it emphasizes the subject's geometric essence and stresses the global aspects of cosmology. Suitable for independent study as well as for courses in differential geometry, relativity, and cosmology. 1979 edition.
Mathematics of Gravitation: Lorentzian geometry and Einstein equations
Author:
Publisher:
Published: 1997
Total Pages: 250
ISBN-13:
DOWNLOAD EBOOKA Mathematical Journey to Relativity
Author: Wladimir-Georges Boskoff
Publisher: Springer Nature
Published: 2020-06-01
Total Pages: 412
ISBN-13: 3030478947
DOWNLOAD EBOOKThis book opens with an axiomatic description of Euclidean and non-Euclidean geometries. Euclidean geometry is the starting point to understand all other geometries and it is the cornerstone for our basic intuition of vector spaces. The generalization to non-Euclidean geometry is the following step to develop the language of Special and General Relativity. These theories are discussed starting from a full geometric point of view. Differential geometry is presented in the simplest way and it is applied to describe the physical world. The final result of this construction is deriving the Einstein field equations for gravitation and spacetime dynamics. Possible solutions, and their physical implications are also discussed: the Schwarzschild metric, the relativistic trajectory of planets, the deflection of light, the black holes, the cosmological solutions like de Sitter, Friedmann-Lemaître-Robertson-Walker, and Gödel ones. Some current problems like dark energy are also scketched. The book is self-contained and includes details of all proofs. It provides solutions or tips to solve problems and exercises. It is designed for undergraduate students and for all readers who want a first geometric approach to Special and General Relativity.
General Relativity and the Einstein Equations
Author: Yvonne Choquet-Bruhat
Publisher: Oxford University Press
Published: 2009
Total Pages: 812
ISBN-13: 0199230722
DOWNLOAD EBOOKGeneral Relativity has passed all experimental and observational tests to model the motion of isolated bodies with strong gravitational fields, though the mathematical and numerical study of these motions is still in its infancy. It is believed that General Relativity models our cosmos, with a manifold of dimensions possibly greater than four and debatable topology opening a vast field of investigation for mathematicians and physicists alike. Remarkable conjectures have been proposed, many results have been obtained but many fundamental questions remain open. In this monograph, aimed at researchers in mathematics and physics, the author overviews the basic ideas in General Relativity, introduces the necessary mathematics and discusses some of the key open questions in the field.
