Another reputable textbook, which I am not familiar with but which other posters have recommended in the past. I am not familiar with this book, but it seems to be a concise but reasonably comprehensive and modern introduction, covering among other things the connection between Moebius transformations and the Lorentz group. This book is notable for making a serious attempt to provide an introduction to both SR and GR, using only basic algebra and calculus no tensors.
It does treat some aspects of some exact solutions in GR but does not adequately cover the field equations and thus cannot be considered a suitable GR text. But it may be helpful to the timorous reader attempting to make the transition from SR to GR. This book is devoted to a rigorous mathematical treatment of the flat Minkowski spacetime of special relativity. It pays particular attention to the Lorentz group and the causal structure of the theory, but also treats the electromagnetic field tensor, spinors, and the topology of Minkowski spacetime. This book won't teach you much physics, but is useful if you want to see special relativity put on a firm mathematical basis, or examine some of the more intricate technical implications of Lorentz transformations or SR causality.
I would not recommend the Dover reprint by Aharoni outdated, poorly written, clumsy notation. I am not familiar with the Dover reprint by Shadowitz. Now we are starting to get to the really good stuff! A beautifully illustrated, clearly and concisely written introduction to GR the first few chapters, on SR, are too sketchy to be valuable except as a review. On balance, I think this is probably the best introduction for the average undergraduate student at present.
It features a particularly well balanced selection of topics. This book covers fewer topics than d'Inverno but in greater depth, and at a comparable level. In places I find it a bit more turgid than some other texts, but Schutz's discussion of the geometric nature of tensors in general and the matter tensor in particular is outstanding. Probably a bit more demanding than d'Inverno , this is probably the best organized GR textbook yet to appear.
The Special Theory of Relativity, A Mathematical Exposition - Dimensions
Clearly written and well translated from the original German , featuring a well balanced selection of topics, and full of useful insight. One of the most concise introductions available. Covers much less than Stephani or d'Inverno , but clear and well written. Advanced undergraduate to beginning gradate level. The textbook of choice for the discerning graduate student. Well written, with a good selection of topics, including careful discussions of tensor formalism, the basic singularity, stability, and uniqueness theorems, as well as black hole thermodynamics.
But I think every serious student must own this at least as a supplementary text and dip into it on a regular basis. MTW was the first "modern" GR textbook, and has inspired two generations of students. While in many respects it is now rather out of date, and in a few places is pretty darn confusing, this beautifully illustrated book features fascinating insights found nowhere else on almost every one of its odd pages. All of these books have exercises; DINV is particular well suited for self study since it also has solutions in the back.
And I'd recommend MTW to anyone, anywhere, any time. For the convenience of the rank beginner who wants to purchase one or more of these textbooks, here is a very rough guide to the coverage: all of these books introduce tensors, including the matter and Riemann and Ricci tensors. All discuss geodesics, connections and covariant derivatives.
The special theory of relativity : a mathematical exposition
All discuss the Equivalence Principle, weak field theory, and at least one interpretation of the field equations. All discuss the classic predictions such as light bending, perihelion advance, gravitational redshift. Among the exact solutions, all discuss in some detail the "usual suspects" Schwarzschild vacuum and Friedmann dust. All discuss the linearized theory of gravitational waves and Cartan's method of curvature forms.
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Five of the six textbooks also discuss at length various of the following important topics: spinors, algebraic symmetries of tensors, the variational principle formulation of GR, the initial value formulation of GR, the Petrov classification of curvature types, EXACT gravitational wave solutions, the singularity theorems, Penrose diagrams conformal compactification , Hawking radiation, and thermodynamics of black holes. Among exact solutions beyond "the usual suspects", DINV features detailed discussions of the Kerr-Newman vacuum, Reissner-Nordstrom electrovac, Tolman fluid, de Sitter and anti-de Sitter cosmological solutions.
HT also features a particularly clear and concise treatment of the Bianchi classification of homogeneous spacelike hyperslices. While I think the six books listed above are among the best currently available textbooks, there are several others worthy of special mention.
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Since the only way to learn a mathematical theory is by doing problems, the more the merrier, this book is an invaluable resource for serious students. Presents the bare essentials geodesics, curvature, the field equation, "the usual suspects" in a concise and accessible manner.
But it uses coordinate notation exclusively, and thus cannot be considered a "modern" introduction despite the date of publication , but it can be good place to learn the essential! Yes, that Dirac. In his inimitable, incredibly concise style, Dirac offers a sixty page sketch of GR, with all the math but not a single picture. First published in , this book doesn't cover any of the modern developments in the subject.
If you are very impatient and have a very strong background in advanced calculus and some differential geometry, this just might be the right book for you. Otherwise it will sail right over your head. No exercises. Most GR books follow more or less in Einstein's footsteps in motivating the field equation.
These authors take a different approach which has become increasingly important in recent years; they motivate the linearized field equation by a careful formal analogy with Maxwell's theory of electromagnetism, and then argue their way to the full field equation. Strong on the important formal analogies with EM, but weak on geometry.
It also has one of the best treatments to be found among introductory GR texts of the experimental and observational consequences of the theory, along with a nice discussion of newtonian gravity. The General Theory of Relativity: A Mathematical Exposition will serve readers as a modern mathematical introduction to the general theory of relativity. Throughout the book, examples, worked-out problems, and exercises with hints and solutions are furnished.
His major areas of research include, among diverse topics, the mathematical aspects of general relativity theory. His research interests include quantum gravity, classical gravity, and semi-classical gravity. Delphenich, Mathematical Reviews, May, An exhaustive list of references and a good index support the text.
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Summing Up: Recommended. Sadanand, Choice, Vol. We have a dedicated site for Germany. Based on courses taught at the University of Dublin, Carnegie Mellon University, and mostly at Simon Fraser University, this book presents the special theory of relativity from a mathematical point of view. It begins with the axioms of the Minkowski vector space and the flat spacetime manifold. Then it discusses the kinematics of special relativity in terms of Lorentz tranformations, and treats the group structure of Lorentz transformations. Extending the discussion to spinors, the author shows how a unimodular mapping of spinor vector space can induce a proper, orthochronous Lorentz mapping on the Minkowski vector space.
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The second part begins with a discussion of relativistic particle mechanics from both the Lagrangian and Hamiltonian points of view.