Short Course in General Relativity

ISBN-10: 0387260781

ISBN-13: 9780387260785

Edition: 3rd 2006 (Revised)

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Description: Suitable for a one-semester course in general relativity for senior undergraduates or beginning graduate students, this text clarifies the mathematical aspects of Einstein's theory of relativity without sacrificing physical understanding. The text begins with an exposition of those aspects of tensor calculus and differential geometry needed for a proper treatment of the subject. The discussion then turns to the spacetime of general relativity and to geodesic motion. A brief consideration of the field equations is followed by a discussion of physics in the vicinity of massive objects, including an elementary treatment of black holes and rotating objects. The main text concludes with introductory chapters on gravitational radiation and cosmology. This new third edition has been updated to take account of fresh observational evidence and experiments. It includes new sections on the Kerr solution (in Chapter 4) and cosmological speeds of recession (in Chapter 6). A more mathematical treatment of tensors and manifolds, included in the 1st edition, but omitted in the 2nd edition, has been restored in an appendix. Also included are two additional appendixes "Special Relativity Review" and "The Chinese Connection" - and outline solutions to all exercises and problems, making it especially suitable for private study.

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Book details

List price: $79.95
Edition: 3rd
Copyright year: 2006
Publisher: Springer
Publication date: 8/30/2005
Binding: Paperback
Pages: 292
Size: 6.00" wide x 9.00" long x 0.50" tall
Weight: 0.946
Language: English

Nightingale is a member of the Physics Dept. at SUNY, New Paltz.

Preface
Introduction
Vector and tensor fields
Introduction
Coordinate systems in Euclidean space
Suffix notation
Tangents and gradients
Coordinate transformations in Euclidean space
Tensor fields in Euclidean space
Surfaces in Euclidean space
Manifolds
Tensor fields on manifolds
Metric properties
What and where are the bases?
The spacetime of general relativity and paths of particles
Introduction
Geodesics
Parallel vectors along a curve
Absolute and covariant differentiation
Geodesic coordinates
The spacetime of general relativity
Newton's laws of motion
Gravitational potential and the geodesic
Newton's law of universal gravitation
A rotating reference system
Field equations and curvature
Introduction
The stress tensor and fluid motion
The curvature tensor and related tensors
Curvature and parallel transport
Geodesic deviation
Einstein's field equations
Einstein's equation compared with Poisson's equation
The Schwarzschild solution
Physics in the vicinity of a massive object
Introduction
Length and time
Radar sounding
Spectralshift
General particle motion (including photons)
Perihelion advance
Bending of light
Geodesic effect
Blackholes
Other coordinate systems
Rotating objects; the Kerr solution
Gravitational radiation
Introduction
What wiggles?
Two polarizations
Simple generation and detection
Elements of cosmology
Introduction
Robertson-Walker line element
Field equations
The Friedmann models
Redshift, distance, and speed of recession
Objects with large redshifts
Comment on Einstein's models; inflation
Newtonian dust
Appendices
Special relativity review
Introduction
Lorentz transformations
Relativistic addition of velocities
Simultaneity
Time dilation, length contraction
Spacetime diagrams
Some standard 4-vectors
Doppler effect
Electromagnetism
The Chinese connection
Background
Lanchester'stransporteronaplane
Lanchester'stransporteronasurface
A trip at constant latitude
Tensors and Manifolds
Introduction
Vector spaces
Dualspaces
Tensor products
The space <$>T_s^r<$>
From tensors to tensor fields
Manifolds
The tangent space at each point of a manifold
Tensor fields on a manifold
Solutions
References
Index
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