Belinski, Vladimir

Prof. Vladimir Belinski

Born: 26 March 1941 in USSR, original nationality Russian, now citizen of Italy

Profile: theoretical physicist specialized in General Relativity and Cosmology
Position: Research Supervisor at the National Institute for Nuclear Physics (INFN), Rome, Italy and member of the International Network of Centres for Relativistic Astrophysics  (ICRANET) in Pescara, Italy.

Official addresses

Prof. V. A. Belinski
National Institute for Nuclear Physics (INFN), Rome Section,
c/o Physics Department, Rome University "La Sapienza",
Piazzale Aldo Moro, 5
00185 Rome, Italy

Prof. V.A.Belinski,
International Network of Centres for Relativistic Astrophysics  (ICRANET)
Piazza della Repubblica, 10
65122  Pescara  (PE), Italy.  

Office Tel: +39-085-23054202 (direct),  
+39-085-23054200 (secretary)
e-mail: , 


1948/09-1958/05, elementary and high school

1958/09-1965/08, student at Moscow Engineering Phyisical Institute

1965/09-1968/09, postgraduate student at Moscow Phyisical-Technical Institute and Landau Institute for Theoretical Physics, Moscow


1968/10-1969/10, engineer at Moscow Institute for Optical-Physical Measurements

1969/10, first scientific degree "Candidate of Physical-Mathematical Sciences" from Landau Institute

1969/11-1981/11, junior researcher, senior researcher at Landau Institute

1981/12, second scientific degree "Doctor of Physical-Mathematical Sciences" from Landau Institute

1981/12-1990/10, "Leading Researcher" at Landau Institute

1989/10-1990/10, Visiting Professor at Yukawa Institute for Theoretical Physics, Kyoto, Japan (on leave from Landau Institute)

1990/11- up to now, Research Supervisor at the National Institute for Nuclear Phisics (INFN), Rome University, Italy.

2005/03-up to now, member of International Network of Centres for Relativistic Astrophysics  (ICRANET) in Pescara, Italy.


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.

Main publications

1. V.A. Belinski and I.M. Khalatnikov "On the Nature of the Singularities in the  General Solution of the Gravitational Equations", Sov. Phys. JETP, 29, 911 (1969) [Russian  Zh. Eksp. Teor. Fiz., 56, 1701 (1969)]. 

2. V.A. Belinski and I.M. Khalatnikov "General Solution of the Gravitational Equations with a Physical Singularity", Sov. Phys. JETP, 30, 1174 (1970) [ Russian Zh. Eksp. Teor. Fiz., 57, 2163 (1969)]. 

3. V.A. Belinski, I.M. Khalatnikov and E.M. Lifshitz "Oscillatory Approach to a Singular Point in the Relativistic Cosmology", Adv. in Phys., 19, 525 (1970). 

4. V.A. Belinski, I.M. Khalatnikov and E.M. Lifshitz "A General Solution of the Einstein Equations with a Time Singularity", Adv. in Phys., 31, 639 (1982). 

5. V. Belinski and V. Zakharov "Integration of the Einstein Equations by means of the inverse scattering problem technique and construction of exact soliton solu­tions". Sov. Phys. JETP, 48, 985, (1978).

6. V. Belinski and V. Zakharov "Stationary gravitational solitons with axial sym­metry". Sov. Phys. JETP, 50, 1, (1979).

7. V. Belinsky, L. Grishchuk, I. Khalatnikov and Y. Zeldovich "Inflationary Stages in Cosmological Models with a scalar Field" Phys. Lett., 155B, 232, (1985).

8. V. Belinski and E. Verdaguer, "Gravitational Solitons", Cambridge University Press, Cambridge Monographs on Mathematical Physics, (2001).

9. V.Belinsky "Gravitational breather and topological properties of gravisolitons". Phys. Rev., D44, 3109, (1991).

10. V.Belinski "On the existence of quantum evaporation of a black hole", Phys. Lett., A209, 13,  (1995).

11. V.A. Belinski, B.M. Karnakov, V.D. Mur and N.B. Narozhnyi "Does the Unruh effect exist ?", JETP Letters, 65, 902 (1997).

12. N.B. Narozhny, A.M. Fedotov, B.M. Karnakov, V.D. Mur and V.A. Belinski, "Boundary conditions in the Unruh problem", Phys. Rev. D65, 025004, (2002).

13. M. V. Barkov, V.A. Belinski and G.S. Bisnovatyi-Kogan, "An exact General Relativity solution for the Motion  and Intersections of Self-Gravitating Shells in the  Field of a Massive Black Hole", JETP 95, 371, (2002).

14. V.A. Belinski,  N.B. Narozhny,  A.M. Fedotov and  V.D. Mur  "Unruh quantization in presence of a condensate",  Phys. Lett. A331, 349, (2004).

15.  M. V. Barkov, G. S. Bisnovatyi-Kogan, A. I. Neishtadt and V.A. Belinski "On chaotic behavior of gravitating stellar shells", Chaos, 15, 013104 (2005).

16. V.A.Belinski, "On the existence of black hole evaporation yet again", Phys. Lett. A354, 249, (2006).