Spacetime: Foundations of General Relativity and Differential Geometry (Lecture Notes in Physics Monographs)
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.
From the Back Cover
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 insights obtained are applied to black hole astrophysics, thereby making the connection to current active research in mathematical physics and cosmology. --This text refers to the Hardcover edition.
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Top customer reviews
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).
The book is most suited for mathematical physicists and theoretical physicists who wish to actually understand the mathematics and the principles involved.
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