Problems of relativistic cosmology

E.M. Lifshitz, I.M. Khalatnikov^a
^aLandau Institute for Theoretical Physics, Russian Academy of Sciences, ul. Kosygina 2, Moscow, 119334, Russian Federation

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 P_[i]αβ[/i] 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

PACS: 98.80.Jk, 04.20.Dw, 04.20.Jb, 04.25.Nx, 04.30.Nk (all)
DOI: 10.1070/PU1964v006n04ABEH003585
URL: https://ufn.ru/en/articles/1964/4/d/
Citation: Lifshitz E M, Khalatnikov I M "Problems of relativistic cosmology" Sov. Phys. Usp. 6 495–522 (1964)

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Оригинал: Лифшиц Е М, Халатников И М «Проблемы релятивистской космологии» УФН 80 391–438 (1963); DOI: 10.3367/UFNr.0080.196307d.0391

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