Exact Solutions of Einstein's Field EquationsCambridge University Press, 24 սեպ, 2009 թ. A paperback edition of a classic text, this book gives a unique survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources. It introduces the foundations of differential geometry and Riemannian geometry and the methods used to characterize, find or construct solutions. The solutions are then considered, ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties. Includes all the developments in the field since the first edition and contains six completely new chapters, covering topics including generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics. It can also be used as an introductory text on some mathematical aspects of general relativity. |
Բովանդակություն
Spatiallyhomogeneous perfect fluid cosmologies 210 | 1 |
Twisting vacuum solutions 437 | 3 |
5 | 5 |
Generation techniques 129 | 6 |
basic concepts | 19 |
Stationary gravitational fields 275 | 23 |
Application of generation techniques to general | 34 |
1 | 35 |
70 | 41 |
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Common terms and phrases
1-forms algebraically special antisymmetric axioms basis vectors bivector bundle Chapter charts classification commutation coefficients complex conjugate complex null tetrad connection coefficients coordinate basis covariant derivative curvature tensor curve y(t defined denoted differentiable manifold differential equations differential geometry directional derivatives ds² dual embedding class energy-momentum tensor Energy-momentum tensors versus exact solutions exterior derivative exterior product Əxi Əyi fibre fluid solutions function f given groups of motions groups on non-null indices run Killing vectors known exact Lie derivative methods metric n-dimensional neighbourhood null tetrad orbits perfect fluids Petrov types Petrov types versus pure radiation fields reader real number respect Rgab Ricci tensor Riemannian space space-time spinor symmetry tangent vector tensor fields tensor of type tensors versus groups theory transformations types versus groups V₁ vacuum solutions vector field Weyl tensor