First Course in General Relativity

ISBN-10: 0521887054

ISBN-13: 9780521887052

Edition: 2nd 2009

Authors: Bernard Schutz
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Description: Clarity, readability and rigor combine in the second edition of this widely-used textbook to provide the first step into general relativity for undergraduate students with a minimal background in mathematics. Topics within relativity that fascinate astrophysical researchers and students alike are covered with Schutz's characteristic ease and authority - from black holes to gravitational lenses, from pulsars to the study of the Universe as a whole. This edition now contains discoveries by astronomers that require general relativity for their explanation; a revised chapter on relativistic stars, including new information on pulsars; an entirely rewritten chapter on cosmology; and an extended, comprehensive treatment of modern detectors and expected sources. Over 300 exercises, many new to this edition, give students the confidence to work with general relativity and the necessary mathematics, whilst the informal writing style makes the subject matter easily accessible. Password protected solutions for instructors are available at www.cambridge.org/9780521887052.

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Book details

List price: $44.99
Edition: 2nd
Copyright year: 2009
Publisher: Cambridge University Press
Publication date: 5/14/2009
Binding: Hardcover
Pages: 406
Size: 7.50" wide x 10.00" long x 1.00" tall
Weight: 2.288
Language: English

Preface to the second edition
Preface to the first edition
Special relativity
Fundamental principles of special relativity (SR) theory
Definition of an inertial observer in SR
New units
Spacetime diagrams
Construction of the coordinates used by another observer
Invariance of the interval
Invariant hyperbolae
Particularly important results
The Lorentz transformation
The velocity-composition law
Paradoxes and physical intuition
Further reading
Appendix: The twin 'paradox' dissected
Exercises
Vector analysis in special relativity
Definition of a vector
Vector algebra
The four-velocity
The four-momentum
Scalar product
Applications
Photons
Further reading
Exercises
Tensor analysis in special relativity
The metric tensor
Definition of tensors
The (01) tensors: one-forms
The (02) tensors
Metric as a mapping of vectors into one-forms
Finally: (MN) tensors
Index 'raising' and 'lowering'
Differentiation of tensors
Further reading
Exercises
Perfect fluids in special relativity
Fluids
Dust: the number-flux vector N
One-forms and surfaces
Dust again: the stress-energy tensor
General fluids
Perfect fluids
Importance for general relativity
Gauss' law
Further reading
Exercises
Preface to curvature
On the relation of gravitation to curvature
Tensor algebra in polar coordinates
Tensor calculus in polar coordinates
Christoffel symbols and the metric
Noncoordinate bases
Looking ahead
Further reading
Exercises
Curved manifolds
Differentiable manifolds and tensors
Riemannian manifolds
Covariant differentiation
Parallel-transport, geodesics, and curvature
The curvature tensor
Bianchi identities: Ricci and Einstein tensors
Curvature in perspective
Further reading
Exercises
Physics in a curved spacetime
The transition from differential geometry to gravity
Physics in slightly curved spacetimes
Curved intuition
Conserved quantities
Further reading
Exercises
The Einstein field equations
Purpose and justification of the field equations
Einstein's equations
Einstein's equations for weak gravitational fields
Newtonian gravitational fields
Further reading
Exercises
Gravitational radiation
The propagation of gravitational waves
The detection of gravitational waves
The generation of gravitational waves
The energy carried away by gravitational waves
Astrophysical sources of gravitational waves
Further reading
Exercises
Spherical solutions for stars
Coordinates for spherically symmetric spacetimes
Static spherically symmetric spacetimes
Static perfect fluid Einstein equations
The exterior geometry
The interior structure of the star
Exact interior solutions
Realistic stars and gravitational collapse
Further reading
Exercises
Schwarzschild geometry and black holes
Trajectories in the Schwarzschild spacetime
Nature of the surface r = 2M
General black holes
Real black holes in astronomy
Quantum mechanical emission of radiation by black holes: the Hawking process
Further reading
Exercises
Cosmology
What is cosmology?
Cosmological kinematics: observing the expanding universe
Cosmological dynamics: understanding the expanding universe
Physical cosmology: the evolution of the universe we observe
Further reading
Exercises
Summary of linear algebra
References
Index
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