Experts Plebäski and Krasi¿ski 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…mehr
Experts Plebäski and Krasi¿ski 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.
Jerzy Plebäski (1928-2005) 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 Plebäski-Demiäski metric), formulation of the heavenly equations and the effective field theory relating GR and supergravity, known as Plebäski action. The first part of the book is developed from Plebäski's lecture notes.
Inhaltsangabe
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.
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.
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