PROBLEMS OF RELATIVISTIC COSMOLOGY

Abstract

CONTENTS I. Features of cosmological solutions of the gravitational equations 495 1. Introduction 495 2. General solution with fictitious singularity 496 3. Anisotropic solution with singularity 500 4. Quasi-isotropic solution 504 5. General conclusions concerning singularities of cosmological solutions 505 II. Gravitational stability of the isotropic world 506 6. Initial model and equations of small perturbations 506 7. Expansion in plane waves 509 8. Perturbations with variation of density of matter 509 9. Rotational perturbations 514 10. Gravitational waves 514 Appendices 514 A. Expansion of the solution of the gravitational equations near a regular point 514 B. Solutions that depend on one variable 515 C. Three-dimensional Ricci tensor Pαβ 516 D. Next terms of the expansion of the anisotropic solution 517 E. Stability of anisotropic solution 518 F. Origin of other types of singularities 519 G. Examples of singularities in exact solutions 520 I. Equations of small perturbations of the gravitational field 521 Cited literature 522