Research activity

V. Belinski is a theoretical physicist specialized in General Relativity and Cosmology and had published about 80 scientific papers in these fields and one book. He is best known for two research results:

1. The proof that there exist singularity of infinite curvature in the general solution of the Einstein equations, and the discovery of oscillatory chaotic structure of that singularity (1968-1975, with E.M.Lifshitz and I.M.Khalatnikov).
   This problem appeared around 85 years ago when the first exactly solvable cosmological models revealed the presence of the Big Bang singularity. Since that time the fundamental question has arisen whether this phenomenon is due to the special simplifying assumptions underlying the exactly solvable models or if a singularity is a general property of the Einstein  equations. The problem was solved by V. Belinski, I. Khalatnikov  and E. Lifshitz (BKL) who showed that a singularity is an unavoidable property of the general cosmological solution of the gravitational equations and not a consequence of the special symmetric structure of exact models. Most importantly BKL were able to find the analytical structure of this generic solution and showed that its behaviour is of an extremely complex oscillatory character, of chaotic type.
   These results have a fundamental significance not only for Cosmology but also for evolution of collapsing matter forming a black hole. The last  stage of collapsing matter in general will follow the BKL regime.
   The BKL analysis provides the description of intrinsic properties of the Einstein equations which can be relevant also in the quantum context. Recently it has been shown that the BKL regime is inherent not only to   General Relativity but also to more general physical theories, such as the superstring models.
   This groundbreaking discovery has created an important field of research which has been continuously active. During the last 38 years the BKL theory of the cosmological singularity has attracted the active attention of the scientific community.
2. The implantation of the Inverse Scattering Method into General Relativity and discovery of gravitational solitons (1977-1982, with V.E.Zakharov).
   Solitons are some remarkable solutions of certain nonlinear wave equations which behave in several ways like extended particles. Soliton waves where first found in some two-dimensional nonlinear differential equations in fluid dynamics. In the 60's a method, known as the Inverse Scattering Method (ISM) was developed. In the late 70's due to the work of V.Belinski and V.Zakharov (BZ) the ISM was extended to General Relativity to solve Einstein equations in vacuum for two-dimensional space-times that admit an orthogonally  transitive two-parameter group of isometries.  These metrics include quite different physical situations such as some cosmological, cylindrically symmetric, colliding plane waves, and stationary axisymmetric solutions. Among the soliton solutions generated by the ISM are some of the most relevant in gravitational physics. Thus in the stationary axisymmetric case the Kerr and Schwarzschild black hole solutions and their generalizations are soliton solutions. Later by the efforts of many authors the BZ method have been extended to the electro-vacuum case, Yang-Mills fields, multidimensional space-time. This field are developing continuously.