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\title{The Negative Energy of Gravitation as Stabilizational Factor in Field Theory
and Cosmology}
\author{Zahid Zakir \\
%EndAName
Institute of Noosphere,\\
167a, B.Ipak Yuli, Tashkent 700187 Uzbekistan}
\maketitle

\begin{abstract}
The left hand side of Einstein's equations G=-T is defined as the tensor of
energy-momentum of gravitational field. Here the energy density of
gravitation is negative, the full energy of the system matter+gravitation is
equal to zero and appeared a new process - the annihilation of matter and
gravitation. As result, the cosmological constant is vanished, singularities
not exist and black holes annihilated during the collaps. It is shown, that
in field theories not need in mass renormalization because of automatical
compensation of infinities by their own gravitational energy. The main
surprise is the renormalizability of quantum gravity with negative energy of
gravitational background.
\end{abstract}

\thispagestyle{empty}

{\bf 1. Introduction.}

{\bf \ 2. The energy-momentum tensor of gravitational field.}

{\bf \ 3. Cosmological constant is vanished.}

{\bf \ 4. Boson dominance in SUSY breaking.}

{\bf \ 5. Singularities and Black Holes are annihilated.}

{\bf \ 6. Gravitational renormalisations in field theories.}

{\bf \ 7. Renormalizable Quantum Gravity.}

{\bf \ 8. Conclusions.}

{\bf \ 9. References}

\section{Introduction}

In the recent papers \cite{ZZ} I attempt to describe the string theories as
statistical mechanics of point particles on some background with finite
temperature. The second step of such thermodynamical description may be
representation of gravitation as some diffusion process on this medium. In
the forthcoming paper the gravitation will be analyzed in framework of
Nelson's stochastic description of quantum fluctuations \cite{Ne} and it
will be shown that gravitation and quantum fluctuations are not independent
phenomena and that the gravitation can be represented as the
nonhomogeneosity of stochastic space-time, i.e. as the consequence of
quantum fluctuations.

The description of gravitation as some diffusion process leads to the
interesting solution for the problem of energy-momentum tensor of
gravitation. {\it The tensor of energy-momentum density of diffusional
gravitation must be negative defined,} because of diffusional flow of energy
always directed from the high energy density regions to the low energy
regions. {\it The full energy-momentum tensor of the system
matter+gravitational field is vanished (nonnegative)}, since the
energy-momentum tensor of gravitation fully compensated the energy-momentum
tensor of the source of this field.

The negative defined energy-momentum tensor for gravitation firstly was
proposed by H.Lorentz \cite{Lo} and T.Levi-Civita \cite{LC} for the
Einstein's equations in general relativity. This proposal is interesting by
itself and in this paper we discuss consequences of this version of general
relativity for the gravitational phenomena, field theory and cosmology.

\section{The energy-momentum tensor of gravitational field.}
 
The tensor of energy-momentum density of gravitational field can be defined
from the Einstein's equations:

\begin{equation}
\frac 1\kappa (R_{ik}-\frac 12g_{ik}R)=-T_{ik} 
\end{equation}

as left hand side of this equations:

\begin{equation}
G_{ik}=\frac 1\kappa (R_{ik}-\frac 12g_{ik}R) 
\end{equation}

   Then the full energy of the system (gravitational field and other matter) is
cancelled:

\begin{equation}
G_{ik}+T_{ik}=0 
\end{equation}

   This form of the tensor of energy-momentum for gravitation was proposed
firstly by H.A.Lorentz \cite {Lo} in 1916 and T.Levi-Chivita \cite {LC} in 1917.

   The energy of gravitons included into $T_{ik}$, while the energy of
gravitational waves included into $G_{ik}$ at large distances from the
source. So, the gravitons we treat as ''matter'' with positive energy, the
gravitational waves treat as variations of the metric with negative energy
density. This treatment is natural in Kaluza-Klein theories, where exist
only gravitons in high dimensions and after the reduction into low
dimensional manifold appeared other particles as some particular forms of
gravitons.

   The stability of the system guarantied only by intrinsic dynamics, described
by Einstein's equations. The creation of matter can be ''organized'', if we
can split the space-time into gravitation and other forms of matter. We can
annihilate the matter with gravitation, if we can pack the energy of
gravitational field of the system into small volume.

\section{Cosmological constant is vanished.}

   One of main problems of unified theories is vanishing of observed value of
the cosmological constant. The unified theories based on the supersymmetry
and all such theories predicted nonzero values of cosmological constant
after breaking of supersymmetry. The models of grand unification and
electroweek theory also predicted large values of cosmological constant.

In our version of gravitational energy this problem solved naturally.
Breaking of the symmetry means the existence of condensate of particles with
some energy density, which leads to the contribution to cosmological
constant $\lambda _m.$ But this energy density of matter induced the
negative energy of gravitational field of particles of the condensate, which
leads to the equivalent contribution to cosmological constant $\lambda _g$
but with opposite sign, and which fully compensated the contribution of
particles.

The Einstein's equations for condensate are:

\begin{equation}
-\lambda _g\cdot g_{ik}=-\lambda _m\cdot g_{ik} 
\end{equation}

and

\begin{equation}
-\lambda \cdot g_{ik}=(-\lambda _g+\lambda _m)\cdot g_{ik}=0 
\end{equation}

This compensation is valid for all kinds of sources of cosmological constant
- for classical and quantum systems. Therefore, the vanishing of the full
energy of the system matter+gravitational field, and particularly, vanishing
of cosmological constant, is some theorem, which indicates existence of a
new type of symmetry - the symmetry between the matter and gravitation, i.e.
between the matter and space-time geometry.

\section{Boson dominance in SUSY breaking.}

The contribution of the fermions into the vacuum energy density is negative.
Therefore, the pure fermionic vacuum is unstable, because of full
cosmological constant $\lambda $ of the matter -$\lambda _f$ and gravitation
is very large and negative:

\begin{equation}
-\lambda _g=\lambda _f 
\end{equation}

and 
\begin{equation}
\lambda =-\lambda _g-\lambda _f\ll 0 
\end{equation}

In the systems of bosons and fermions the stable vacuum exist only if the
bosonic contribution to the energy of vacuum condensate $\lambda _b$ is
larger than the contribution of fermionic part $\lambda _f:$

\begin{equation}
\lambda =-\lambda _g+(\lambda _b-\lambda _f)=0 
\end{equation}

This fact we may call as {\it rule of boson dominance in supersymmetry
breaking. }

In case of pure supersymmetry we have

\begin{equation}
\lambda _b-\lambda _f=\lambda _m=0 
\end{equation}

and $\lambda _g=0.$

\section{Singularities and Black Holes are annihilated.}

The particle and it's gravitational field annihilated near the singularity
point inside of the black hole and {\it therefore the singularities vanished
in the classical gravitational theory.}

The process of annihilation of all particles inside of the black hole leads
to the decreasing of an area of the horizon and radius with speed of light.
The external gravitational field of the black hole partly released from the
source and will be emitted as gravitational waves and particles (gravitons). 
{\it Therefore, the black holes annihilated during the process of their
formation by emission of strongly gravitational waves and high energy
gravitons. }This effect may by observed in case of some astrophysical
objects.

\section{Gravitational renormalizations in field theories.}

In calculations of the energy levels in quantum field theory appeared some
infinities, which usually can be excluded be renormalization of masses and
charges of particles \cite{Bi}. In our version of gravitational energy, each
infinity contribution to the energy of the field or particle induced
infinite contribution to the energy of background gravitational field with
opposite sign, which exactly compensated contributions to the energy of
matter.

Therefore, we can conclude, that negative defined energy of gravitation is
main renormalizational factor for the quantum field theory, and the
procedures of renormalization can ce obtained from the first principles of
the field theory, if we include into Lagrangian gravitational part.

\section{Renormalizable quantum gravity.}

We have one quantum field theory, where problem of renormalization of energy
is very important and unsolvable by ordinary methods. This is quantum
gravity. But the surprising fact is the renormalizability of quantum gravity
in case of negative defined energy of gravitational field.

The contributions of gravitons have positive energy and we treat this part
as ''matter'' contribution $T_{ik}^{(g)}.$ All infinities in all orders of
perturbation theory induced infinite background gravitational fields with
opposite sign contributions to the energy of vacuum and fully compensated
the ''matter'' contributions.

\section{Conclusions}

The observable consequences of this theory are vanishing of cosmological
constant and the black holes annihilation during the process of their
formation by emission of strongly gravitational waves and high energy
gravitons. The last effect may by observed in case of some astrophysical
objects.

\begin{thebibliography}{9}
\bibitem{ZZ}  {hep-th/9809170, Zakir Z. {\it Thermostring Quantization.
Interpretation of Strings as Particles at Finite Temperature.}
hep-th/9810247, Zakir Z. {\it Are Strings Thermostrings? }}

\bibitem{Ne}  {Nelson E. (1966) Phys.Rev. v.150, p.1079.}

\bibitem{Lo}  {Lorentz H.A. (1916) Versl.Akad.Amsterdam, v.25, p.468;\\
Lorentz H.A. (1937) Collected {Papers.} The Hague: M.Nijhoff, v.5, p.276-313.}
\bibitem{LC}  {Levi-Civita T. (1917) Rend.Acc.Lincei, ser.5a, v.XXVI,p.381.}

\bibitem{Bi}  {Birrell N.D., Davies P. (1982) {\it Quantum Fields in Curved
Space.}, Camb.U.Pr.}
\end{thebibliography}

\end{document}
