Gravitation in Weyl-Integrable Spaces
Physical processes taking place in very strong gravitational
fields have received much attention in recent years. Many theoretical models
of such processes, based on General Relativity as the standard gravitational
theory, are troubled by the problem of the appearance of unavoidable
singularities. It is well known that the classical description
provided by General Relativity is no
longer valid when large space-time curvatures do occur
(V.P.Frolov,
M.A.Markov, e V.F.Mukhanov, Physical Review D 41, 383, 1990). In the
attempt to overcome such difficulties, modifications of General Relativity
have been proposed, in particular string theories and multidimensional
Kaluza-Klein theories. These approaches give rise to
the Dilaton field theory, where the strength of a neutral scalar field
determines the values of coupling constants in the four-dimensional effective
theory. It has been established that this theory is the low-energy
limit of string theory, when
electromagnetic interactions are present (D.Garfinkle,
G.T.Horowitz e A.Strominger, Physical Review D 43, 3140, 1991; G.W.Gibbons
e K.Maeda, Nuclear Physics B 298, 741, 1988; J.H.Horne e G.T.Horowitz,
Physical Review D 46, 1340, 1992), or also as the result of dimensional
reduction
of multidimensional Kaluza-Klein theories (R.Sorkin, Physical Review
Letters 51, 87, 1983; D.Gross e M.J.Perry, Nuclear Physics B 226, 29, 1983).
Afterwards, Dilaton theory was enlarged to include the case of a second
scalar field, taken to represent matter interacting with
gravity (Z.Tao
e X.Xue, Physical Review D 45, 1878, 1992). The presence of the Dilaton
may be seen as a drawback in the formal structure of General Relativity,
in the sense that it spoils one of the most beautiful results of this theory:
the geometrization of the gravitational interaction. This
difficulty can be avoided if the Riemmanian space-time
structure of General Relativity is generalized. It should be stressed,
though, that such generalization is not an arbitrary artifact, introduced
for accomplishing the geometrization of the Dilaton field. In fact, it
is due to a distinct and independent motivation put forth by Ehlers et
al. (J.Ehlers, F.Pirani e A.Schild, General Relativity, Ed. L.O'Raifeartaigh,
Oxford, Clarendon, 1982). These authors sought for an axiomatic formulation
for determining the structure of space-time,making use of simple, fundamental
elements such as free-falling particles and light rays; the geometrical
structure thus obtained was not Riemman's, but Weyl's integrable geometry.
The latter differs from Riemman geometry by allowing length transportation
to become space-time point dependent. A scalar (Dilaton) field appears,
in this case, as a natural consequence of the assumed fundamental axioms
and is assimilated to the affine nature of the new geometry. Its purely
geometrical character is thus ensured. Making use of this space-time representation,
a theory of gravitation is built in which the
gravitational
interaction
is completely geometrized (M.Novello, L.A.R.Oliveira, J.M.Salim e E.Elbaz,
International Journal of Modern Physics D 1, 641, 1993; J.M.Salim e S.L.Sautú,
Classical and Quantum Gravity 13, 353, 1996). The presence of this scalar
field changes large-scale gravitational
processes, so as to require a renewed study of some typical
gravitational configurations, such as spherically symmetric solutions,
both neutral and charged (J.M.Salim e S.L.Sautú, Classical and Quantum
Gravity 15, 203, 1998), homogeneous and isotropic cosmological models (H.P.Oliveira,
J.M.Salim
e S.L.Sautú, Classical and Quantum Gravity 14, 2833, 1998),
as well as anisotropic solutions in the presence of magnetic fields (J.M.Salim,
S.L.Sautú e R.Martins, Classical and Quantum Gravity 15, 1521, 1998).
In many cases, the Dilaton field made it possible to eliminate
singularities that showed up in the corresponding General
Relativity solutions, and further provided for the natural generation of
inflationary phases in cosmological solutions (J.C.Fabris, J.M.Salim
e S.L.Sautú, Modern Physics Letters A 13, 953, 1998). Next, modifications
induced in the
background radiation by the presence of the geometrical
scalar field will be studied, particularly with regard to the determination
of its polarization (M.Zaldarriaga
e D.D.Harari, Physical Review D 52, 3276, 1995). An analytical treatment
describing cosmic microwave radiation polarization
must then be established, taking into account the interaction
with the Dilaton field. Furthermore, this study should be enlarged to account
for the additional Faraday rotation due to the Dilaton. To do so, both
the formalism describing cosmic microwave radiation (M.Giovannini,
Physical
Review
D 56, 3198, 1997) and studies upon Faraday gravitational rotation in
the presence of a Dilaton in stationary space-times (M.Nouri-Zonoz,
Physical Review D 60, 024013-1, 1999) shall be applied. In the future,
the aim is to build cosmological models derived from the
solutions thus obtained (J.C.Fabris, J.M.Salim e S.L.Sautú,
Modern Physics Letters A 13, 953, 1998), to compare this models with observational
data, to study the stability of the models and the problem of structure
formation. Further cosmological enquiries shall investigate anisotropic
models and possible isotropization effects due to or
associated to the Dilaton field; in particular, the issue of particle production
induced by the Dilaton field and its influence on isotropization.