20 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
FRW Universe Models in Conformally Flat Spacetime Coordinates. III: Universe models with positive spatial curvature
We deduce general expressions for the line element of universe models with
positive spatial curvature described by conformally flat spacetime coordinates.
Models with dust, radiation and vacuum energy are exhibited. Discussing the
existence of particle horizons we show that there is continual annihilation of
space, matter and energy in a dust and radiation dominated universe, and
continual creation in a LIVE domined universe when conformal time is used in
Friedmann-Robertson-Walker models with positive spatial curvature. A general
procedure is given for finding coordinates to be used in Penrose diagrams. We
also calculate the age and the redshift of some universe models using conformal
time.Comment: 22 pages, 9 figure
A Conserved Bach Current
The Bach tensor and a vector which generates conformal symmetries allow a
conserved four-current to be defined. The Bach four-current gives rise to a
quasilocal two-surface expression for power per luminosity distance in the
Vaidya exterior of collapsing fluid interiors. This is interpreted in terms of
entropy generation.Comment: to appear in Class. Quantum Gra
Palatini versus metric formulation in higher curvature gravity
We compare the metric and the Palatini formalism to obtain the Einstein
equations in the presence of higher-order curvature corrections that consist of
contractions of the Riemann tensor, but not of its derivatives. We find that
there is a class of theories for which the two formalisms are equivalent. This
class contains the Palatini version of Lovelock theory, but also more
Lagrangians that are not Lovelock, but respect certain symmetries. For the
general case, we find that imposing the Levi-Civita connection as an Ansatz,
the Palatini formalism is contained within the metric formalism, in the sense
that any solution of the former also appears as a solution of the latter, but
not necessarily the other way around. Finally we give the conditions the
solutions of the metric equations should satisfy in order to solve the Palatini
equations.Comment: 13 pages, latex. V2: reference added, major changes in section 3,
conclusions partially correcte
Covariant conservation of energy momentum in modified gravities
An explicit proof of the vanishing of the covariant divergence of the
energy-momentum tensor in modified theories of gravity is presented. The
gravitational action is written in arbitrary dimensions and allowed to depend
nonlinearly on the curvature scalar and its couplings with a scalar field. Also
the case of a function of the curvature scalar multiplying a matter Lagrangian
is considered. The proof is given both in the metric and in the first-order
formalism, i.e. under the Palatini variational principle. It is found that the
covariant conservation of energy-momentum is built-in to the field equations.
This crucial result, called the generalized Bianchi identity, can also be
deduced directly from the covariance of the extended gravitational action.
Furthermore, we demonstrate that in all of these cases, the freely falling
world lines are determined by the field equations alone and turn out to be the
geodesics associated with the metric compatible connection. The independent
connection in the Palatini formulation of these generalized theories does not
have a similar direct physical interpretation. However, in the conformal
Einstein frame a certain bi-metricity emerges into the structure of these
theories. In the light of our interpretation of the independent connection as
an auxiliary variable we can also reconsider some criticisms of the Palatini
formulation originally raised by Buchdahl.Comment: 8 pages. v2: more discussio
Naked Singularity in a Modified Gravity Theory
The cosmological constant induced by quantum fluctuation of the graviton on a
given background is considered as a tool for building a spectrum of different
geometries. In particular, we apply the method to the Schwarzschild background
with positive and negative mass parameter. In this way, we put on the same
level of comparison the related naked singularity (-M) and the positive mass
wormhole. We discuss how to extract information in the context of a f(R)
theory. We use the Wheeler-De Witt equation as a basic equation to perform such
an analysis regarded as a Sturm-Liouville problem . The application of the same
procedure used for the ordinary theory, namely f(R)=R, reveals that to this
approximation level, it is not possible to classify the Schwarzschild and its
naked partner into a geometry spectrum.Comment: 8 Pages. Contribution given to DICE 2008. To appear in the
proceeding
Extracting the Cosmological Constant from the Wheeler DeWitt Equation in a Modified Gravity Theory
We discuss how to extract information about the cosmological constant from
the Wheeler-DeWitt equation, considered as an eigenvalue of a Sturm-Liouville
problem. A generalization to a f(R)theory is taken under examination. The
equation is approximated to one loop with the help of a variational approach
with Gaussian trial wave functionals. We use a zeta function regularization to
handle with divergences. A renormalization procedure is introduced to remove
the infinities together with a renormalization group equation.Comment: Talk given at QFEXT 07, Workshop on Quantum Field Theory Under the
Influence of External Conditions, Leipzig, 17-21 Sep 2007 and talk given at
9th International Conference on Path Integrals - New Trends and Perspectives,
Dresden, 23-28 September 2007. 8 pages, accepted for publication in Journal
of Physics
A Unified Approach to Variational Derivatives of Modified Gravitational Actions
Our main aim in this paper is to promote the coframe variational method as a
unified approach to derive field equations for any given gravitational action
containing the algebraic functions of the scalars constructed from the Riemann
curvature tensor and its contractions. We are able to derive a master equation
which expresses the variational derivatives of the generalized gravitational
actions in terms of the variational derivatives of its constituent curvature
scalars. Using the Lagrange multiplier method relative to an orthonormal
coframe, we investigate the variational procedures for modified gravitational
Lagrangian densities in spacetime dimensions . We study
well-known gravitational actions such as those involving the Gauss-Bonnet and
Ricci-squared, Kretchmann scalar, Weyl-squared terms and their algebraic
generalizations similar to generic theories and the algebraic
generalization of sixth order gravitational Lagrangians. We put forth a new
model involving the gravitational Chern-Simons term and also give three
dimensional New massive gravity equations in a new form in terms of the Cotton
2-form
A Kinematical Approach to Conformal Cosmology
We present an alternative cosmology based on conformal gravity, as originally
introduced by H. Weyl and recently revisited by P. Mannheim and D. Kazanas.
Unlike past similar attempts our approach is a purely kinematical application
of the conformal symmetry to the Universe, through a critical reanalysis of
fundamental astrophysical observations, such as the cosmological redshift and
others. As a result of this novel approach we obtain a closed-form expression
for the cosmic scale factor R(t) and a revised interpretation of the space-time
coordinates usually employed in cosmology. New fundamental cosmological
parameters are introduced and evaluated. This emerging new cosmology does not
seem to possess any of the controversial features of the current standard
model, such as the presence of dark matter, dark energy or of a cosmological
constant, the existence of the horizon problem or of an inflationary phase.
Comparing our results with current conformal cosmologies in the literature, we
note that our kinematic cosmology is equivalent to conformal gravity with a
cosmological constant at late (or early) cosmological times. The cosmic scale
factor and the evolution of the Universe are described in terms of several
dimensionless quantities, among which a new cosmological variable delta emerges
as a natural cosmic time. The mathematical connections between all these
quantities are described in details and a relationship is established with the
original kinematic cosmology by L. Infeld and A. Schild. The mathematical
foundations of our kinematical conformal cosmology will need to be checked
against current astrophysical experimental data, before this new model can
become a viable alternative to the standard theory.Comment: Improved version, with minor changes. 58 pages, including 7 figures
and one table. Accepted for publication in General Relativity and Gravitation
(GERG