Einstein SpacesEinstein Spaces presents the mathematical basis of the theory of gravitation and discusses the various spaces that form the basis of the theory of relativity. This book examines the contemporary development of the theory of relativity, leading to the study of such problems as gravitational radiation, the interaction of fields, and the behavior of elementary particles in a gravitational field. Organized into nine chapters, this book starts with an overview of the principles of the special theory of relativity, with emphasis on the mathematical aspects. This text then discusses the need for a general classification of all potential gravitational fields, and in particular, Einstein spaces. Other chapters consider the gravitational fields in empty space, such as in a region where the energy-momentum tensor is zero. The final chapter deals with the problem of the limiting conditions in integrating the gravitational field equations. Physicists and mathematicians will find this book useful. |
Contents
| 1 | |
Chapter 2 Einstein Spaces | 67 |
Chapter 3 General Classification of Gravitational Fields | 88 |
Chapter 4 Motions in Empty Space | 132 |
Chapter 5 Classification of General Gravitational Fields by Groups of Motions | 198 |
Chapter 6 Conformal Mapping of Einstein Spaces | 257 |
Chapter 7 Geodesic Mapping of Gravitational Fields | 276 |
Chapter 8 The Cauchy Problem for the Einstein Field Equations | 303 |
Chapter 9 Special Types of Gravitational Field | 342 |
| 385 | |
| 407 | |
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Common terms and phrases
3-matrix A. Z. PETROV Abelian admit a G algebraic allowed transformations arbitrary functions bitensor bivector space canonical form Cauchy data classification coefficients complex conformal const constant curvature contravariant coordinate system corresponding covariant derivative curvature tensor curve defined denoted determined domain Einstein space elementary divisors energy-momentum tensor eqns example field equations flat space following theorem geodesic geometry gravitational fields group of motions Hence holonomic hypersurface identical independent intransitive introduce invariant isotropic Killing equations Killing vector linear Lorentz manifolds mapping Math matrix metric ds metric signature metric tensor Minkowski space necessary and sufficient non-isotropic non-zero orthogonal orthonormal tetrad parameters Phys possible principal directions reduced Riemann spaces satisfy scalar curvature Segre characteristic set of equations shows signature solution space of constant space-time spaces admitting structure equations subgroup surfaces of transitivity symmetric system of coordinates T2 spaces theory of relativity tions two-dimensional zero