Flat and Curved Space-Times 2nd Edition by George F. R. Ellis (PDF)

Description

The present book explains special relativity and the basics of general relativity from a geometric viewpoint. Space-time geometry is emphasized throughout, and provides the basis of understanding of the special relativity effects of time dilation, length contraction, and the relativity of simultaneity. Bondi’s K-calculus is introduced as a simple means of calculating the magnitudes of these effects, and leads to a derivation of the Lorentz transformation as a way of unifying these results. The invariant interval of flat space-time is generalised to that of curved space-times, and leads to an understanding of the basic properties of simple cosmological models and of the collapse of a star to form a black hole. The appendices enable the advanced student to master the application of four-tensors to the relativistic study of energy and momentum, and of electromagnetism. In addition, this new edition contains up-to-date information on black holes, gravitational collapse, andcosmology.

User’s Reviews

Editorial Reviews: About the Author G.F.R. Ellis, Professor of Mathematics, University of Cape Town, South Africa. R.M. Williams, Assistant Director of Research, Department of Applied Mathematics and Theoretical Physics, University of Cambridge

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The year is 1978: publication of Robert Geroch’s book, General Relativity From A to B. A decade later: publication of this book, Flat and Curved Space-Times, mentioning that Geroch’s exposition is close in spirit to the present enterprise (that spirit– geometrical outlook). One may ask, then, how do they differ ? After all, both publications are outstanding examples of semi-technical (or, semi-popular–depending on your viewpoint ) expository prose. The books complement each other: Geroch, in my view, provides ideal preliminary to this exposition. Geroch’s book is stepping stone to this one. Furthermore, Ellis and Williams serves as stepping stone to more advanced treatments (examples: continue on with Taylor and Wheeler’s Space Time Physics, then, Hartle’s textbook of Gravity).(1) Let us begin with the three Appendices, A, B, C: They are calculus based and more mathematical than the entire preceding exposition. Offered here is explication of topics such as line integrals, four-vectors, four-tensors, electromagnetism and energy-momentum conservation. Read: “the principle of relativity was already embedded in the classical theory, indeed it forms the foundation of the well-known relation between electricity and magnetism.” (page 127).(2) As with Geroch’s elementary book, the beginning chapters here move slowly (up to page 100) making sure to detail the kinematics of special relativity, we read: “only the whole package is consistent.” (example: Muon decay). Read this bit of wisdom: “There are two separate ways of going about– the first relies on working out in detail how all space and time measurements alter when one changes from one reference frame to another. The second approach takes what is in effect the opposite viewpoint–is there any feature of the space-time that is unchanged by an arbitrary change of reference frame?Are there Invariant features ? ” (page 107).(3) Chapter four details each of two viewpoints: Lorentz transformations (first viewpoint) and invariant interval (second viewpoint). This chapter (four) utilizing only algebra, should be required reading for all students of physics regardless of specialty. A highlight, the enlightening discussion of two-dimensional Rindler universe: “it displays some of the features of a Black Hole.” (page 180).(4) Final, fifth chapter, introduction to curvature and the equivalence principle: “if one uses a flat-space description, one can only mimic the effect of gravity everywhere by having available infinitely many accelerating frames.” (page 206). A fine section ensues regarding tidal effects and geodesic deviation. Metric, field equations, causality: all discussed here in exemplary fashion (required reading for all Physics students). Spherical stars and collapse, read: “the theory we are using predicts a singularity.”Simple cosmological models occupy seventh chapter. Regards inflationary model “this is just the steady-state universe model in a new disguise ! ” (page 284).(5) Exercises are scattered throughout the exposition. References for further reading are here. I would be hard-pressed to recommend a better expository account of basics, including exercises, utilizing merely basic mathematics. For the layman, for physics and mathematics students, for seasoned researchers, this book offers something for everyone. The illustrations and figures, plentiful throughout, are delightful and meaningful. Highly recommended to all.

⭐which is the title of the first Chapter of this book.The two other reviewers have said it all- you will not find a better description for the understanding of space-time diagrams than in this book. page 37: “Space-time diagrams give a very convenient description of spatial and temporal relations, which enable us to clarify important features such a the nature of causal relationships.” And this is just the beginning of this wonderful book.At this writing many 1988 editions, which are fine, for sale on Amazon for a penny. If you want to understand the topics this book covers- buy it and enjoy.

⭐Book was adequately described in ad and arrived in estimated time.

⭐Awesome

⭐Flat and curved Spacetimes is largely an introduction to Special Relativity without requiring many prerequisites. Over half the book focuses on the special theory followed by a brief discussion on the general relativity and curved space times. It also discusses some cosmology and has appendices with some some basic calculus and vector analysis. It is intuitive to read and the exercises are approachable though the computer exercises are outdated.The book largely introduces special relativity by introducing k-calculus and it takes the reader into time dilation and doppler effects via considering the consequences of light signals between different inertial observers. From such simple assumptions the authors derive many important results and discuss the Lorentz transformations. The authors discuss the lack of invariance for simultaneity and concepts like length contraction. The book is very descriptive and though it uses math where needed, one is not overwhelmed with symbolism. The author goes from the Lorentz transformation the invariance of spacetime distance which is the key to special relativity. From there they move onto basic general theory and start with the concept of a geodesic. The authors take the typical approach of discussing curvature of 2-d surfaces embedded in 3-d surfaces to frame the concept of curvature and then discuss how the line element contains the information required to calculate intrinsic curvature. The authors introduce several curved metrics, including the Schwartzchild metric and discuss things like black holes. Though one can follow it, these become more difficult to truly understand compared to the flat spacetime chapters in the first 2/3 of the book. The authors get into cosmology as well which gets to be more challenging and that’s where they leave it.Overall the book is excellent for the novice. There are perhaps some better more recent treatments, the geometry of special relativity, by trevian dray might fall into that category. But this is an excellent treatment that leaves the author with a firm grasp of basic special relativity and some conceptual understanding of the general theory. Definitely recommended.

⭐Another indispensable text for the physicist struggling to understand the fundamental edifice of Relativity. It will also help understanding of Electrodynamics; see especially Appendix C, which elaborates on how the electric and magnetic fields are actually inseparably entwined into a four-tensor, which concept itself is an analogy to the 4-D tensors that comprise the gravitational field.One does not need light speed to work on relativistic concepts. The magnetic field IS AN ELECTRIC FIELD, viewed from a moving frame of reference. Or put another way, the magnetic field is a consequence of relativistic invariance, no need for high speed, relativistic velocities.Many explanations in this text bind together seemingly disparate notions; solid expositions of the principle of equivalence, geodesics and the Schwartzschild solution, among other critical developments.Highly recommended

⭐This book sets out the basic mathematics of relativity in a clear and understandable way. It is not a cheap work either in price or content. I was able to buy this used copy at a small fraction af the new cost and have been pleased to add it to my permanent collection.

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