Experts Plebanski and Krasinski 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.
Experts Plebanski and Krasinski provide a thorough introduction to the tools of general relativity and relativistic cosmology, guiding advanced students through complete derivations of the results. Starting with a short course on differential geometry, the main text describes relativity as a physical theory.
Daugiau informacijos
Experts introduce the tools of GR and relativistic cosmology, guiding advanced students through complete derivations of the results.
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
EinsteinMaxwell equations and the KaluzaKlein 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 RobertsonWalker geometry;
18.
Relativistic cosmology III: the LemaītreTolman geometry;
19. Relativistic
cosmology IV: Simple generalisations of LT 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.
Jerzy Plebaski (19282005) was a Polish theoretical physicist best known for his extensive research into general relativity, nonlinear electrodynamics and mathematical physics. He split his time between Warsaw, Poland, and Mexico, his permanent residence from the mid-1970s onwards. He is remembered, among other things, for defining the algebraic classification of the tensor of matter, for finding new solutions of the Einstein equations (for example, the PlebaskiDemiaski metric), formulation of the heavenly equations and the effective field theory relating GR and supergravity, known as Plebaski action. The first part of the book is developed from Plebaski's lecture notes. Andrzej Krasiski is Emeritus Professor at the Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences in Warsaw. He served for many years on the Editorial Board of the journal 'General Relativity and Gravitation' and has acted as Poland's elected representative on the international committee of the International Society for General Relativity and Gravitation. He is author of Inhomogeneous Cosmological Models (Cambridge, 1997), co-author of Structures in the Universe by Exact Methods (Cambridge, 2009), and co-editor of Golden Oldies in General Relativity (Springer, 2013). His research record includes many papers on the interpretation of inhomogeneous cosmological models. He is also a co-author of a computer program, Ortocartan, for algebraic calculations in general relativity.
