An introduction to general relativity and cosmology

Author(s)

Bibliographic Information

An introduction to general relativity and cosmology

Jerzy Plebański, Andrzej Krasiński

Cambridge University Press, 2012

  • : pbk

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Note

Includes bibliographical references (p. 501-517) and index

Originally published: 2006

Description and Table of Contents

Description

General relativity is a cornerstone of modern physics, and is of major importance in its applications to cosmology. Plebanski and Krasinski are experts in the field and in this book they provide a thorough introduction to general relativity, guiding the reader through complete derivations of the most important results. Providing coverage from a unique viewpoint, geometrical, physical and astrophysical properties of inhomogeneous cosmological models are all systematically and clearly presented, allowing the reader to follow and verify all derivations. For advanced undergraduates and graduates in physics and astronomy, this textbook will enable students to develop expertise in the mathematical techniques necessary to study general relativity.

Table of Contents

  • 1. How the theory of relativity came into being (a brief historical sketch)
  • Part I. Elements of Differential Geometry: 2. A short sketch of two-dimensional differential geometries
  • 3. Tensors, tensor densities
  • 4. Covariant derivatives
  • 5. Parallel transport and geodesic lines
  • 6. Curvature of a manifold: flat manifolds
  • 7. Riemannian geometry
  • 8. Symmetries of Rieman spaces, invariance of tensors
  • 9. Methods to calculate the curvature quickly - Cartan forms and algebraic computer programs
  • 10. The spatially homogeneous Bianchi-type spacetimes
  • 11. The Petrov classification by the spinor method
  • Part II. The Gravitation Theory: 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 field 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 Lemaitre-Tolman geometry
  • 19. Relativistic cosmology IV: generalisations of L-T and related geometries
  • 20. The Kerr solution
  • 21. Subjects omitted in this book
  • References.

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