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ISBN:3642085644
Author: Marcus Kriele
ISBN13: 978-3642085642
Title: Spacetime: Foundations of General Relativity and Differential Geometry (Lecture Notes in Physics Monographs)
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Language: English
Category: Mathematics
Publisher: Springer (December 8, 2010)
Pages: 436

Spacetime: Foundations of General Relativity and Differential Geometry (Lecture Notes in Physics Monographs) by Marcus Kriele



Spacetime Foundations of General and Differential. Author Marcus Kriele. with its 424 pages is meant to cover both general relativity differential geometry. It is therefore clear that. book, pseudo-Riemannian. and. important topics had to be omitted. mathematicians, the most important omissions are certainly some topics peculiar to Riemannian geometry, such as the Hopf-Rinow theorem (O’Neill 1983, Theorem . 1) and the Myers theorem (O’Neill 1983, Theorem 1. 4).

Series: Lecture Notes in Physics Monographs (Book 59). Hardcover: 432 pages. General relativity is the physical expression of differential geometry, an area of mathematics that is quite detailed. It is very important not just to get the formalism firmly in mind, but to get a deeper understanding--an intuitive understanding--of what the whole thing really means. For special relativity, Mermin's book is very good because it gives great clarity for the underlying meaning. There are other wonderful books in the area, and Woodhouse has two very nice and interesting volumes. I have never found any single book that puts forward both the needed mathematics in a clearly.

Lecture Notes in Physics Monographs. Foundations of General Relativity and Differential Geometry. Authors: Kriele, Marcus. This textbook is for mathematicians and mathematical physicists and is mainly concerned with the physical justification of both the mathematical framework and the foundations of the theory of general relativity. Previous knowledge of the relevant physics is not assumed. This book is also suitable as an introduction to pseudo-Riemannian geometry with emphasis on geometrical concepts. A significant part of the text is devoted to the discussion of causality and singularity theorems

The book presents the foundations of special and general relativity from a higherthan standard level of mathematical sophistication. As the author explicitly statesin the preface, he aims at writing a modern textbook on general relativity formathematicians and mathematical physicists with emphasis on the physical jus-tification of the mathematical framework. Also: Knowledge of physics is notassumed. This is certainly a very ambitious programme, comparable perhapsto the well known book by R. Sachs and H. W. .

differential geometry (1) general relativity (2) math (2) mathematical physics (1) physics (1) physique (1) relativity (1). refresh. Member recommendations.

However, case differential pseudo-Riemannian geometry or the general relativity between and mathematics relationship physics is and it is therefore especially close, to from interd- possible profit an ciplinary approach. html?hl ru&id 9LoPBwAAQBAJ. One of the most of exciting aspects is the general relativity pred- tion of black holes and the Such Big Bang. predictions gained weight the theorems through Penrose. singularity pioneered In various by te- books on theorems general relativity singularity are and then presented used to that black holes exist and that the argue universe started with a To date what has big.

Spacetime: Foundations of General Relativity and Differential Geometry (Lecture Notes in Physics). Modern Differential Geometry for Physicists (World Scientific Lecture Notes in Physics). Differential geometry, analysis, and physics. Inflationary Cosmology (Lecture Notes in Physics). Astrométrie moderne (Lecture Notes in Physics 358). Applied Quantum Cryptography (Lecture Notes in Physics). Lecture notes on differential equations of mathematical physics. Differential Geometry in Physics.

This textbook is for mathematicians and mathematical physicists and is mainly concerned with the physical justification of both the mathematical framework and the foundations of the theory of general relativity. A significant part of the text is devoted to the discussion of causality and singularity theorems.

This book is also suitable as an introduction to pseudo-Riemannian geometry with emphasis on geometrical concepts.

One of the most of exciting aspects is the general relativity pred- tion of black holes and the Such Big Bang. predictions gained weight the theorems through Penrose. singularity pioneered In various by te- books on theorems general relativity singularity are and then presented used to that black holes exist and that the argue universe started with a To date what has big been is bang. a critical of what lacking analysis these theorems predict-’ We of really give a proof a typical singul- theorem and this ity use theorem to illustrate problems arising through the of possibilities violations" and "causality weak "shell very crossing These singularities". add to the problems weight of view that the point theorems alone singularity are not sufficient to the existence of predict physical singularities. The mathematical theme of the book In order to both solid gain a of and intuition understanding good for any mathematical theory, one,should to realise it as model of try a a fam- iar non-mathematical theories have had concept. Physical an especially the important on of and impact development mathematics, conversely various modern theories physical rather require sophisticated mathem- ics for their formulation. both and mathematics Today, physics are so that it is often difficult complex to master the theories in both very s- in the of jects. However, case differential pseudo-Riemannian geometry or the general relativity between and mathematics relationship physics is and it is therefore especially close, to from interd- possible profit an ciplinary approach.
Reviews: 3
Ynonno
General relativity is the physical expression of differential geometry, an area of mathematics that is quite detailed. It is very important not just to get the formalism firmly in mind, but to get a deeper understanding---an intuitive understanding---of what the whole thing really means. For special relativity, Mermin's book is very good because it gives great clarity for the underlying meaning. There are other wonderful books in the area, and Woodhouse has two very nice and interesting volumes. I have never found any single book that puts forward both the needed mathematics in a clearly explained way and also the significant underpinnings of the real physics. I'm always looking for a "kinder" "gentler" way to understand relativity, mainly because real insight comes more from understanding the foundations of the theory and less from exploring some niche consequence of the theory. I find this book very helpful indeed and pleasant and rewarding to read. It is unlike other books, and its structure is very helpful.
Qudanilyr
This book deals with the physical justification of the mathematical framework involved in the modern and highly sophisticated theories of the structure of the universe.
The book seems to have been written for working physicists and mathematicians, and maybe for graduate students, but I think most of the material of the first 5 chapters could find a place in undergraduate curricula.
There are some other regarded texts treating this same subjects, but this one attempts to ensure that the mathematical description mirrors the physical concepts involved, so this approach also leads to a careful treatment of the structural aspects of mathematics.
The contents are: Local Theory of Space and Time; Analysis on Manifolds; Space and Time from a Global Point of View; Pseudo-Riemannian Manifolds; General Relativity; Robertson-Walker Cosmology; Spherical Symmetry; Causality; Singularity Theorems.
Includes an extensive list of references and a system of guidelines to read the book, because the author states that it is not meant to be read in the same order as it is written.
Very useful as a reference.
Please take a look at the rest of my reviews (just click on my name above).
Keth
Unlike most other books on general relativity, this one treats Einstein's theory from an actual differential geometric perspective. This means that it is written like a mathematics text book and the author sticks to coordinate independent expressions where possible. Hence there are less messy and lengthy local expressions and, as I see it, it is much clearer what is actually done.
The book is most suited for mathematical physicists and theoretical physicists who wish to actually understand the mathematics and the principles involved.