An Introduction to General Relativity and Cosmology

✍ Scribed by Jerzy Plebanski, Andrzej Krasinski

• Publisher: Cambridge University Press
• Year: 2024
• Tongue: English
• Leaves: 579
• Edition: 2
• Category: Library

✦ Synopsis

Experts Plebański and Krasiński provide a thorough introduction to the tools of general relativity and relativistic cosmology. Assuming familiarity with advanced calculus, classical mechanics, electrodynamics and special relativity, the text begins with a short course on differential geometry, taking a unique top-down approach. Starting with general manifolds on which only tensors are defined, the covariant derivative and affine connection are introduced before moving on to geodesics and curvature. Only then is the metric tensor and the (pseudo)-Riemannian geometry introduced, specialising the general results to this case. The main text describes relativity as a physical theory, with applications to astrophysics and cosmology. It takes the reader beyond traditional courses on relativity through in-depth descriptions of inhomogeneous cosmological models and the Kerr metric. Emphasis is given to complete and clear derivations of the results, enabling readers to access research articles published in relativity journals.

✦ Table of Contents

The scope of this text
Preface to the second edition
Acknowledgements
1. How the theory of relativity came into being (a brief historical sketch)
Part I. Elements of Differential Geometry:
2. A short sketch of 2-dimensional differential geometry
3. Tensors, tensor densities
4. Covariant derivatives
5. Parallel transport and geodesic lines
6. The curvature of a manifold
flat manifolds
7. Riemannian geometry
8. Symmetries of Riemann spaces, invariance of tensors
9. Methods to calculate the curvature quickly: differential forms and algebraic computer programs
10. The spatially homogeneous Bianchi-type spacetimes
11. The Petrov classification by the spinor method
Part II. The Theory of Gravitation:
12. The Einstein equations and the sources of a gravitational field
13. The Maxwell and Einstein–Maxwell equations and the Kaluza–Klein theory
14. Spherically symmetric gravitational fields of isolated objects
15. Relativistic hydrodynamics and thermodynamics
16. Relativistic cosmology I: general geometry
17. Relativistic cosmology II: the Robertson–Walker geometry
18. Relativistic cosmology III: the Lemaître–Tolman geometry
19. Relativistic cosmology IV: Simple generalisations of L–T and related geometries
20. Relativistic cosmology V: the Szekeres geometries
21. The Kerr metric
22 Relativity enters technology: the Global Positioning System
23. Subjects omitted from this book
24. Comments to selected exercises and calculations
References
Index.

✦ Subjects

Physics; Astronomy; Cosmology; Relativity; Gravitation; Theoretical Physics; Mathematical Physics