43 research outputs found
Variational and conformal structure of nonlinear metric-connection gravitational lagrangians
We examine the variational and conformal structures of higher order theories
of gravity which are derived from a metric-connection Lagrangian that is an
arbitrary function of the curvature invariants. We show that the constrained
first order formalism when applied to these theories may lead consistently to a
new method of reduction of order of the associated field equations. We show
that the similarity of the field equations which are derived from appropriate
actions via this formalism to those produced by Hilbert varying purely metric
Lagrangians is not merely formal but is implied by the diffeomorphism covariant
property of the associated Lagrangians. We prove that the conformal equivalence
theorem of these theories with general relativity plus a scalar field, holds in
the extended framework of Weyl geometry with the same forms of field and
self-interacting potential but, in addition, there is a new `source term' which
plays the role of a stress. We point out how these results may be further
exploited and address a number of new issues that arise from this analysis.Comment: 8 pages, LaTeX (REVTeX 3.1), submitted to J. Math. Phys., references
added (nothing changed but LaTeX style
Singularities of varying light speed cosmologies
We study the possible singularities of isotropic cosmological models that
have a varying speed of light as well as a varying gravitational constant. The
field equations typically reduce to two dimensional systems which are then
analyzed both by dynamical systems techniques in phase space and by applying
the method of asymptotic splittings. In the general case we find initially
expanding closed models which recollapse to a future singularity and open
universes that are eternally expanding towards the future. The precise nature
of the singularities is also discussed.Comment: 7 pages, 2 figures, uses iop style files, to appear in the
Proceedings of the Greek Relativity Meeting NEB12, June 29-July 2, 2006,
Nauplia, Greec
Oscillatory behavior of closed isotropic models in second order gravity theory
Homogeneous and isotropic models are studied in the Jordan frame of the
second order gravity theory. The late time evolution of the models is analysed
with the methods of the dynamical systems. The normal form of the dynamical
system has periodic solutions for a large set of initial conditions. This
implies that an initially expanding closed isotropic universe may exhibit
oscillatory behaviour.Comment: 16 pages, 3 figures. With some minor improvements. To appear in
General Relativity and Gravitatio
Conformally flat spacetimes and Weyl frames
We discuss the concepts of Weyl and Riemann frames in the context of metric
theories of gravity and state the fact that they are completely equivalent as
far as geodesic motion is concerned. We apply this result to conformally flat
spacetimes and show that a new picture arises when a Riemannian spacetime is
taken by means of geometrical gauge transformations into a Minkowskian flat
spacetime. We find out that in the Weyl frame gravity is described by a scalar
field. We give some examples of how conformally flat spacetime configurations
look when viewed from the standpoint of a Weyl frame. We show that in the
non-relativistic and weak field regime the Weyl scalar field may be identified
with the Newtonian gravitational potential. We suggest an equation for the
scalar field by varying the Einstein-Hilbert action restricted to the class of
conformally-flat spacetimes. We revisit Einstein and Fokker's interpretation of
Nordstr\"om scalar gravity theory and draw an analogy between this approach and
the Weyl gauge formalism. We briefly take a look at two-dimensional gravity as
viewed in the Weyl frame and address the question of quantizing a conformally
flat spacetime by going to the Weyl frame.Comment: LATEX - 18 page
General Relativity and Weyl Geometry
We show that the general theory of relativity can be formulated in the
language of Weyl geometry. We develop the concept of Weyl frames and point out
that the new mathematical formalism may lead to different pictures of the same
gravitational phenomena. We show that in an arbitrary Weyl frame general
relativity, which takes the form of a scalar-tensor gravitational theory, is
invariant with respect to Weyl tranformations. A kew point in the development
of the formalism is to build an action that is manifestly invariant with
respect to Weyl transformations. When this action is expressed in terms of
Riemannian geometry we find that the theory has some similarities with
Brans-Dicke gravitational theory. In this scenario, the gravitational field is
not described by the metric tensor only, but by a combination of both the
metric and a geometrical scalar field. We illustrate this point by, firstly,
discussing the Newtonian limit in an arbitrary frame, and, secondly, by
examining how distinct geometrical and physical pictures of the same phenomena
may arise in different frames. To give an example, we discuss the gravitational
spectral shift as viewed in a general Weyl frame. We further explore the
analogy of general relativity with scalar-tensor theories and show how a known
Brans-Dicke vacuum solution may appear as a solution of general relativity
theory when reinterpreted in a particular Weyl frame. Finally, we show that the
so-called WIST gravity theories are mathematically equivalent to Brans-Dicke
theory when viewed in a particular frame.Comment: LATEX, 22 page
Accelerated cosmological expansion due to a scalar field whose potential has a positive lower bound
In many cases a nonlinear scalar field with potential can lead to
accelerated expansion in cosmological models. This paper contains mathematical
results on this subject for homogeneous spacetimes. It is shown that, under the
assumption that has a strictly positive minimum, Wald's theorem on
spacetimes with positive cosmological constant can be generalized to a wide
class of potentials. In some cases detailed information on late-time
asymptotics is obtained. Results on the behaviour in the past time direction
are also presented.Comment: 16 page
On the Past Asymptotic Dynamics of Non-minimally Coupled Dark Energy
We apply dynamical systems techniques to investigate cosmological models
inspired in scalar-tensor theories written in the Einstein frame. We prove that
if the potential and the coupling function are sufficiently smooth functions,
the scalar field almost always diverges into the past. The dynamics of two
important invariant sets is investigated in some detail. By assuming some
regularity conditions for the potential and for the coupling function, it is
constructed a dynamical system well suited to investigate the dynamics where
the scalar field diverges, i.e. near the initial singularity. The critical
points therein are investigated and the cosmological solutions associated to
them are characterized. We find that our system admits scaling solutions. Some
examples are taken from the bibliography to illustrate the major results. Also
we present asymptotic expansions for the cosmological solutions near the
initial space-time singularity, which extend in a way previous results of other
researchers.Comment: 38 pages, 2 figures, accepted for publication in CQ
Space-time singularities in Weyl manifolds
We extend one of the Hawking-Penrose singularity theorems in general
relativity to the case of some scalar-tensor gravity theories in which the
scalar field has a geometrical character and space-time has the mathematical
structure of a Weyl integrable space-time (WIST). We adopt an invariant
formalism, so that the extended version of theorem does not depend on a
particular frame.Comment: 16 page