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General relativity is via it’s formulation a theory heavily based on differential geometry. General Theory of Relativity by Dirac gives a 68 page introduction to the mathematical theory of general relativity. The style of the book is “no nonsense” and “uncluttered”. The book is based on series of lectures given by Dirac at Florida State University in 1973. |
The book is aimed at advanced undergraduates, though it will be well suited for beginning graduate students and researchers who want a quick overview of the structure of general relativity.
Chapter 1 to 14 cover topics of differential geometry: parallel displacement, Christoffel symbols, geodesics, covariant derivatives and curvature tensors. All the basics of geometry required for general relativity.
Chapters 15 to 35 deal with the “guts” of general relativity. Topics covered include Einstein’s law of gravity, the Newtonian approximation, gravitational red shift, the Schwarzschild metric & black holes, harmonic coordinates, the field equations with matter, the gravitational action principle, the pesudo energy-tensor for gravity, gravitational waves and the cosmological constant.
Paperback: 68 pages
Publisher: Princeton University Press (January 8, 1996)
Language: English
ISBN-10: 069101146X
ISBN-13: 978-0691011462