An introduction to general relativity and cosmology [E-Book] / Jerzy Plebański, Andrzej Krasiński.
Plebański, Jerzy, (author)
Krasiński, Andrzej, (author)
Cambridge : Cambridge University Press, 2006
1 online resource (xix, 534 pages)
Full Text
Table of Contents:
  • How the theory of relativity came into being (a brief historical sketch)
  • Part I. Elements of differential geometry. A short sketch of 2-dimensional differential geometry ; Tensors, tensor densities ; Covariant derivatives ; Parallel transport and geodesic lines ; The curvature of a manifold, flat manifolds ; Riemannian geometry ; Symmetries of Riemann spaces, invariance of tensors ; Methods to calculate the curvature quickly : Cartan forms and algebraic computer programs ; The spatially homogeneous Bianchi type spacetimes ; The Petrov classification by the spinor method
  • Part II. The theory of gravitation. The Einstein equations and the sources of a gravitational field ; The Maxwell and Einstein : Maxwell equations and the Kaluza-Klein theory ; Spherically symmetric gravitational fields of isolated objects ; Relativistic hydrodynamics and thermodynamics ; Relativistic cosmology I : general geometry ; Relativistic cosmology II : the Robertson-Walker geometry ; Relativistic cosmology III : the Lemaître-Tolman geometry ; Relativistic cosmology IV : generalisations of L-T and related geometries ; The Kerr solution ; Subjects omitted from this book.