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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:
 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 (19681975, 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.
 The implantation of the
Inverse Scattering Method into General Relativity and discovery of
gravitational solitons (19771982, 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 twodimensional 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
twodimensional spacetimes that admit an orthogonally transitive twoparameter 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 electrovacuum case, YangMills fields, multidimensional
spacetime. This field are developing continuously.
