UP
1. Chaotic behaviour of gravitational
field near cosmological singularity
(oscillatory regime, onset of chaos, statistical description)
One of the main our activity is the study of the problem of influence of
inhomogenity on the structure of the general oscillatory regime of gravitational field
near cosmological singularity. It was shown that an unavoidable and unlimited development
of small-scale exitations in asymptotic vicinity to the singularity make the picture very
similar to the highly developed turbulence.
The problems under the current research are: an exact mathematical
formulation of the state of gravitational turbulence in terms of the charachteristic
functional of the random gravitational field in the vicinity of cosmological singularity
and construction of appropriate averaging procedure in order to avoid too detailed
description of the complicated small-scale structure of such gravitational turbulent
regime.
Another direction of the research is the study of the possible
compactification mechanisms in multidimensional inhomogeneous Cosmology.
We developed a detailed study about the influence of different kinds of
"matter" on the initial singularity present in the Friedmann-Robertson-Walker,
quasi-isotropic and generic inhomogenous solution. In particular we considered the effects
of ultrarelativistic matter, particles creation, scalar and vector fields [5].
The most recent results obtained during year 2001-2002 are as follows:
- It has been presented (G. Imponente and G. Montani) a detailed analysis
of the stochastic properties characterizing, near the ''Big-Bang'' the Bianchi type VIII
and IX cosmological models. In particular we have shown the time independence of their
dynamics, as well as of their invariant measure, the choice of a particular temporal gauge
[Ref. 2,3,4]; the achievements of these results is based on an Arnowitt-Deser-Misner
hamiltonian approach, as written in terms of Misner-Chitrè-like variables. In connection
with these subjects, it was provided a straightforward relation between the classical
chaoticity of these two Bianchi models and their indeterministic quantum behavior,
performed during the Planckian era; The physical ground of this result is based on a WKB
approximation, able to reduce the semiclassical quantum probability distribution to the
classical microcanonical one [Ref. 5,6]. For a general review on these investigations, see
[Ref 7].
- On the base of a standard hamiltonian approach, developed adopting
Misner-Chitrè-like variables, is constructed (G. Montani) a solution to the continuity
equation for the Bianchi VIII and IX cosmological models, as written in the asymptotic
limit to the initial "Big-Bang''; the knowledge of this solutions provides the
asymptotic nonstationary corrections to the invariant measure for the system, which result
to decay exponentially [Ref. 8].
UP
2. Influence of the scalar
fields on the cosmological evolution
By the investigation of a ''generic inhomogeneous''
cosmological solution in the presence of a real self-interaction scalar field (expected
responsible for a spontaneous symmetry breaking configuration), it is constructed (A.A.
Kirillov and G. Montani) an interpolating "generic'' solution, able to connect a
"generic'' Kasner-like regime with an inflationary scenario. This result has the
merit to individualize a mechanism for the quasi-isotropization of our universe, i.e. it
allows to understand how it is possible to put in the same dynamical picture the necessity
of a "generic Big-Bang'' (we recall that the FRW model is unstable backward in time
and should admit a spectrum of initial perturbations) and the high homogeneity and
isotropy required by the Standard Cosmological Model [Ref. 10].
UP
3. Macroscopic gravity
(development of the theory of the smeared gravitational and matter fields)
We developed a study of the gravitational polarization phenomenon in the
limit of a perturbative quadratic theory based on a joint Isaacson-Szekeres approach. In
particular we individualized a material relation connecting the Isaacson energy-momentum
tensor with the trace-free component of the quadrupole one.
Results during period 2000-2002 regard are based as follows.
A study of the polarization phenomenon, based on a macroscopic gravity
theory has been developed (G. Montani, R. Ruffini and R Zalaletdinov), in a perturbative
approach, to characterize the correlations existing between the matter quadrupole and the
high frequency radiation terms, both appearing on a second order averaged expansion (the
first order propagative effects vanish on average). The main result of this work is to be
regarded as the individualization of the appropriate "material relations'' for the
background dynamics [Ref. 1].
UP
4. Quantum
effects in external gravitational field and Quantum Gravity
- On the base of criticism to the nature of the Wheeler-Dewitt approach, it
is provided (G. Montani) a reformulation of the quantum geometrodynamics within the
(3+1)-slicing representation of the space-time. The fundamental statement of this analysis
is the necessity to include the so-called "kinematical action'' even in the case of a
quantum space-time, so getting a completely consistent formulation for a
"gauge-fixing'' quantization of the 3-geometries [Ref. 9].
- In order to obtain a vacuum theory of the torsion field of the second
order, as that one of any other field (including the space-time geometry), it is proposed
(G. Aprea, G. Montani, R. Ruffini) a Lagrangian formulation for the space-time geometry,
characterized by a non-riemannian connection (we retain only its totally antisymmetric and
trace components) which is expressed by a scalar and a tensor potential. The obtained
field equations predicts the existence of torsion waves, having interesting implications
on the motion of the test particles, as described by the self-parallel lines [Ref. 11].
- By applying, in the line of the idea proposed by I.Prigogine, the theory
of open thermodynamical systems to an expanding isotropic universe, is provided
(G.Montani) a phenomenolgical approach to the particles creation mechanisms in the very
early cosmology; the main result of this work consists in showing how the horizon paradox
finds a natural solution upon taking into account the matter creation near the big Bang
[Ref. 12].
- It was derived (D.Oriti, R.M. Williams) the the Barrett-Crane spin foam
model for Euclidean 4-dimensional quantum gravity from a discretized BF theory, imposing
the constraints that reduce it to gravity at the quantum level. We obtain in this way a
precise prescription of the form of the Barrett-Crane state sum, in the general case of an
arbitrary manifold with boundary. In particular we derive the amplitude for the edges of
the spin foam from a natural procedure of gluing different 4-simplices along a common
tetrahedron. The generalization of our results to higher dimensions is also shown [Ref.
13].
- E.R. Livine and D.Oriti study a generalized action for gravity as a
constrained BF theory, and its relationship with the Plebanski action. We analyse the
discretization of the constraints and the spin foam quantization of the theory, showing
that it leads naturally to the Barrett-Crane spin foam model for quantum gravity. Our
analysis holds true in both the Euclidean and Lorentzian formulation [Ref. 14].
- D.Oriti made an introduction to spin foam models for non-perturbative
quantum gravity, an approach that lies at the point of convergence of many different
research areas, including loop quantum gravity, topological quantum field theories, path
integral quantum gravity, lattice gauge theory, matrix models, category theory,
statistical mechanics. We describe the general formalism and ideas of spin foam models,
the picture of quantum geometry emerging from them, and give a review of the results
obtained so far, in both the Euclidean and Lorentzian case. We focus in particular on the
Barrett-Crane model for 4-dimensional quantum gravity [Ref. 15].
- D.Oriti extended the lattice gauge theory-type derivation of the
Barrett-Crane spin foam model for quantum gravity to other choices of boundary conditions,
resulting in different boundary terms, and re-analyze the gluing of 4-simplices in this
context. This provides a consistency check of the previous derivation. Moreover we study
and discuss some possible alternatives and variations that can be made to it, and the
problems they present [Ref. 16].
UP
5. Quantum Field Theory
in accelerated frames
By considering quantum theory of the free field in
Minkowski and Rindler spacetimes we show that conventional derivation of the Unruh effect
is not correct since boundary conditions for the fields in these spacetimes are different.
We also show that algebraic approach to this problem leads to the same conclusion. These
results are important because there are serious arguments to think that the Unruh effect
is closely related to the effect of quantum evaporation of black holes.
Results during period 2000-2002 regard are based as
follows.
It was accomplished the final analysis of the so called
Unruh effect both from the point of view of canonical and algebraic approach to the
quantum field theory (N.B. Narozhny, A.M. Fedotov, B.M. Karnakov, V.D. Mur and V.A.
Belinski). It was shown that the quantization procedure proposed by Unruh implies setting
a boundary condition for the quantum field operator and this changes drastically the
topological properties and symmetry group of the spacetime which lead to the field theory
in two disconnected left and right Rindler spacetimes instead of Minkowski spacetime. Thus
in spite of the work over last 25 years, there still remain serious gaps in grounding of
the Unruh effect, and as of now there is no compelling evidence for the universal
behaviour attributrd to all uniformly accelerated detectors [Ref. 17].
UP
6. Collapse of stellar
clusters and mass run away effect
- It was investigated a model of ballistic ejection effect of matter from
spherically symmetric stellar clusters (M. V. Barkov, V.A. Belinski and G.S.
Bisnovatyi-Kogan). The problem was solved in newtonian gravity but with cutoff fixing the
minimal radius of selfgravitating matter shell by its relativistic gravitational radus. It
was shown that during the motion of two initially gravitationally bound spherical shells,
consisting of point particles moving along ballistic trajectories, one of the shell may be
expelled to infinity at subrelativistic expelling velocity of the order of 0,25c. Also it
was shown that the motion of two intersecting shells in the case when they do not runaway
shows a chaotic behaviour [Ref. 18].
- It was found (M. V. Barkov, V.A. Belinski and G.S. Bisnovatyi-Kogan) the
complete exact solution in the General Relativity for the intersection process of two
massive selfgravitating spherically symmetric shells (in general with tangential
pressure). It was shown how one can calculate all shell’s parameters after
intersection in terms of the parameters before the intersection. The result is quite new,
the solution of this kind was known only for the massless shells (Dray and t’Hooft,
1985). The solution was applied to the analysis of matter ejection effect from
relativistic stellar clusters and to the chaotic motion of the shells in relativistic
regime. It was shown that in relativistic case the matter ejection effect is stronger than
in newtonian gravity [Ref. 19].
UP
7.
Gravitational and Electromagnetogravitational solitons
This research line is the further development of
the theory of gravitational solitons. Here the research is going in the following three
drections. First, it was already established the existence of the gravisolitonic
topological charge. However the exact mathematical formulation of this phenomenon
(especially the exact expression for the topological current) is still remain to be seen.
Second, the possibility of the quantum creation of gravisolitons near the cosmological
singularity is under investigation. Third, we are intending to construct the well defined
energetics of gravisolitons.
Results during period 2000-2002 regard are based as
follows.
- It was accomplished the final version of the book "Gravitational
Solitons" (V. Belinski and E. Verdaguer). Here is a self-contained exposition of the
theory of gravitational solitons and provides a comprehensive review of exact soliton
solutions to Einstein's equations. The text begins with a detailed discussion of the
extension of the Inverse Scattering Method to the theory of gravitation, starting with
pure gravity and then extending it to the coupling of gravity with the electromagnetic
field. There follows a systematic review of the gravitational soliton solutions based on
their symmetries. These solutions include some of the most interesting in gravitational
physics such as those describing inhomogeneous cosmological models, cylindrical waves, the
collision of exact gravity waves,and the Schwarzschild and Kerr black holes [Ref. 20].
- The Alexeev approach for the construction of Electromagnetogravisolitons
was elaborated and translated to the conventional Belinski-Zakharov method. The results
was included as one of the chapter to the book "Gravitational Solitons" [Ref.
20].
UP
SELECTED
PUBLICATIONS (1970-2000):
- V.Belinski, I.Khalatnikov and E.Lifshitz:
"Oscillatory Approach to a Singular Point in the Relativistic Cosmology",
Advances in Physics, 19, 525, 1970;
- V.Belinski, I.Khalatnikov and E.Lifshitz: "A
General Solution of the Einstein Equations with a Time Singularity", Advances in
Physics, 31, 639, 1982;
- 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;
- V.Belinski and V.Zakharov: "Stationary
gravitational solitons with axial symmetry", Sov.Phys. JETP, 50, 1, 1979;
- V.Belinski: "Gravitational breather and
topological properties of gravisolitons" Phys. Rev. D, 44, 3109, 1991;
- V.Belinski and R.Ruffini: "Radiation from a
relativistic Magnetized Star", Astrophys.Journal Letters, 401, L27, 1992;
- V.Belinski, F. de Paolis, H.W.Lee and R.Ruffini:
"Radiation from a Relativistic Rotanting Magnetic Dipole. Magnetic Synchroton
Effect", Astron.Astrophys., 283, 1018, 1994;
- V.Belinski: "On the development of
gravitational turbolence near the cosmological singularity", JETP Letters, 56, 421,
1982;
- V.Belinski and G.Montani: "A Scenario of
Dimensional Compactification near the Cosmological Singularity", preprint I.C.R.A.,
July 1993;
- V.Belinski: "On the existence of black hole
evaporation", 1) Phys.Lett.A, submitted, 1994; 2) The talk given at Proc.of the
seventh Marcel Grossmann Meeting, Stanford, USA, 1994; 3) The short version submitted to
the Proc.of the seventh Marcel Grossmann Meeting, Stanford, USA, 1994;
- G.Montani: "On the General Behaviour of the
Universe Near Cosmological Singularity", Classical and Quantum Gravity, 12, 2503,
(1995).
- V.Belinski, B.M.Karnakov, V.D. Mur, N.B.
Narozhnyi:"Does the Unruh effect exist?", JETP Letters, 65, 902 (1997).
- G. Montani "On the singularity problem in
cosmology", Nuovo Cimento, 112B, 459, (1997)
- A. Kirillov and G. Montani "Description of
statistical properties of the mixmaster universe", Phys. Rev. D56, 6225, (1997)
- A. Kirillov and G. Montani "Origin of a
classical space in quantum inhomogeneous models", JETP Lett. 66, 475, (1997)
- G. Montani "On the quasi-isotropic solution
in the presence of ultrarelativistic matter and a scalar field", Classical and
Quantum Gravity, 16, 723, (1999)
- A.Fedotov, V.Mur, N. Narozhny, V. Belinski, B.
Karnakov, "Quantum field aspect of the Unruh problem", Phys. Lett. A254, 126,
(1999)
- N. Narozhny, A. Fedotov, B. Karnakov, V. Mur and
V. Belinski, "Boundary conditions in the Unruh problem", hep-th/9906181, (1999)
- Bini D., Gemelli G., Ruffini R., Spinning test
particles in general relativity: nongeodesic motion in the Reissner-Nordstr"om
spacetime, Physical Review D, vol. 61, 064013, 2000.
- Bini D., Jantzen R.T., Circular orbits in Kerr
spacetime: equatorial plane embedding diagrams, Classical and Quantum Gravity, vol 17,
1-11, 2000.
- Bini D., de Felice F., Gyroscopes and
gravitational waves, Classical and Quantum Gravity, vol 17, 4627-4635, 2000.
- Bini D., Jantzen R.T. Gravitoelectromagnetism: a
tool for observer-dependent interpretation of spacetime physics,. Il Nuovo Cimento, vol
115B, n. 070809, Luglio-Settembre 2000, pag.713.
- Bini D., de Felice F. Gyroscopes and Gravitational
Waves, in Gravitational Waves, Ed. by I. Ciufolini, V. Gorini, U. Moschella, P. Fre, IOP,
Pub., 2000. Cap. 15, pag 268-279.
UP
Publications
Jan. 2001- Jan. 2002
- G. Montani, R. Ruffini and R.M.
Zalaletdinov "Gravitating macroscopic media in general relativity and 2001, 115 B, N.
11, 1343.
- G.Imponente and G. Montani, " Covariance of
the mixmaster chaoticity", Physical Review D., 2001, 63,103501.
- G.Imponente and G. Montani, "Covariant
Formulation of the Invariant Measure for the Mixmaster Dynamics", submitted to
Physics Letters A, on October 2001
- G.Imponente and G. Montani, "Covariant
Mixmaster Dynamics", in "Similarities and Universality in Relativistic
Flows", Ed. by Logos Verlag, Berlin (2001).
- G.Imponente and G. Montani, " On the Quantum
Origin of the Mixmaster Chaos Covariance", 2002, Nuclear Phys. B Proc. Suppl. 104,
193-196
- G.Imponente and G. Montani, "Mixmaster
Chaoticity as Semiclassical Limit of the Canonical Quantum Dynamics", submitted to
Classical and Quantum Gravity, on December 2001
- G.Imponente and G.Montani, "Mixmaster Chaos
and Quantum Aspects of the Statistical Probability Distribution", 2001, International
Journal of the Korean Physical Society, in press.
- G. Montani, "Nonstationary correction to the
mixmaster model invariant measure'', accepted by Nuovo Cimento B, January 2002, in press.
- G. Montani, "Canonical quantization of
gravity without "frozen formalism'', submitted to Nuclear Physics B, January 2002.
- A.A. Kirillov and G. Montani,
"Quasi-isotropization of the inhomogeneous mixmaster Universe induced by an
inflationary process'', submitted to Physics Review D, January 2002.
- G. Aprea, G. Montani and R. Ruffini,
"Lagrangian formulation of a geometrical theory with torsion'', in preparation.
- G. Montani, "Influence of the particle
creation on the flat and negative curved FLRW universes" Class.and Quantum Grav.,
2001, 18, 193.
- D.Oriti, R.M. Williams, "Gluing 4-simplices:
a derivation of the Barrett-Crane spin foam model for Euclidean quantum gravity",
Phys. Rev. D 63, 024022 (2001); gr-qc/0010031;
- E.R. Livine, D. Oriti, "Barrett-Crane spin
foam model from generalized BF-type action for gravity'', to appear in Phys. Rev. D;
gr-qc/0104043
- D. Oriti, "Spacetime geometry from algebra:
spin foam models for non-perturbative quantum gravity'', Rep. Prog. Phys. 64, 1489,
(2001), gr-qc/0106091;
- D. Oriti, "Boundary terms in the
Barrett-Crane spin foam model and consistent gluing'', submitted for publication;
gr-qc/0201xxx (to appear in the e-archives in these days)
- 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.
- M. V. Barkov, V.A. Belinski and G.S.
Bisnovatyi-Kogan, "Chaotic motion and ballistic ejection of gravitating shells",
astro-ph/0107051, submitted to "Monthly Notices".
- M. V. Barkov, V.A. Belinski and G.S.
Bisnovatyi-Kogan, "The exact solution in General Relativity for the motion and
intersections of the selfgravitating shells in the external field of the massive black
hole", submitted to Sov. Phys. JETP.
- V. Belinski and E. Verdaguer, "Gravitational
Solitons", Cambridge University Press, Cambridge Monographs on Mathematical Physics,
2001.
UP