375 research outputs found
The interior spacetimes of stars in Palatini f(R) gravity
We study the interior spacetimes of stars in the Palatini formalism of f(R)
gravity and derive a generalized Tolman-Oppenheimer-Volkoff and mass equation
for a static, spherically symmetric star. We show that matching the interior
solution with the exterior Schwarzschild-De Sitter solution in general gives a
relation between the gravitational mass and the density profile of a star,
which is different from the one in General Relativity. These modifications
become neglible in models for which is a decreasing function of R however. As a result, both Solar System
constraints and stellar dynamics are perfectly consistent with .Comment: Published version, 6 pages, 1 figur
Symmetric hyperbolic systems for a large class of fields in arbitrary dimension
Symmetric hyperbolic systems of equations are explicitly constructed for a
general class of tensor fields by considering their structure as r-fold forms.
The hyperbolizations depend on 2r-1 arbitrary timelike vectors. The importance
of the so-called "superenergy" tensors, which provide the necessary symmetric
positive matrices, is emphasized and made explicit. Thereby, a unified
treatment of many physical systems is achieved, as well as of the sometimes
called "higher order" systems. The characteristics of these symmetric
hyperbolic systems are always physical, and directly related to the null
directions of the superenergy tensor, which are in particular principal null
directions of the tensor field solutions. Generic energy estimates and
inequalities are presented too.Comment: 24 pages, no figure
G\"{o}del-type universes in f(R) gravity
The gravity theories provide an alternative way to explain the current
cosmic acceleration without a dark energy matter component. If gravity is
governed by a theory a number of issues should be reexamined in this
framework, including the violation of causality problem on nonlocal scale. We
examine the question as to whether the gravity theories permit
space-times in which the causality is violated. We show that the field
equations of these gravity theories do not exclude solutions with
breakdown of causality for a physically well-motivated perfect-fluid matter
content. We demonstrate that every perfect-fluid G\"{o}del-type solution of a
generic gravity satisfying the condition is necessarily
isometric to the G\"odel geometry, and therefore presents violation of
causality. This result extends a theorem on G\"{o}del-type models, which has
been established in the context of general relativity. We also derive an
expression for the critical radius (beyond which the causality is
violated) for an arbitrary theory, making apparent that the violation of
causality depends on both the gravity theory and the matter content. As
an illustration, we concretely take a recent gravity theory that is free
from singularities of the Ricci scalar and is cosmologically viable, and show
that this theory accommodates noncausal as well as causal G\"odel-type
solutions.Comment: 7 pages, V3: Version to appear in Phys. Rev. D (2009), typos
corrected, the generality of our main results is emphasized. The illustrative
character of a particular theory is also made explici
Galactic rotation curves in modified gravity with non-minimal coupling between matter and geometry
We investigate the possibility that the behavior of the rotational velocities
of test particles gravitating around galaxies can be explained in the framework
of modified gravity models with non-minimal matter-geometry coupling.
Generally, the dynamics of test particles around galaxies, as well as the
corresponding mass deficit, is explained by postulating the existence of dark
matter. The extra-terms in the gravitational field equations with
geometry-matter coupling modify the equations of motion of test particles, and
induce a supplementary gravitational interaction. Starting from the variational
principle describing the particle motion in the presence of the non-minimal
coupling, the expression of the tangential velocity of a test particle, moving
in the vacuum on a stable circular orbit in a spherically symmetric geometry,
is derived. The tangential velocity depends on the metric tensor components, as
well as of the coupling function between matter and geometry. The Doppler
velocity shifts are also obtained in terms of the coupling function. If the
tangential velocity profile is known, the coupling term between matter and
geometry can be obtained explicitly in an analytical form. The functional form
of this function is obtained in two cases, for a constant tangential velocity,
and for an empirical velocity profile obtained from astronomical observations,
respectively. Therefore, these results open the possibility of directly testing
the modified gravity models with non-minimal coupling between matter and
geometry by using direct astronomical and astrophysical observations at the
galactic or extra-galactic scale.Comment: 8 pages, accepted for publication in PR
Quantization of the Maxwell field in curved spacetimes of arbitrary dimension
We quantize the massless p-form field that obeys the generalized Maxwell
field equations in curved spacetimes of dimension n > 1. We begin by showing
that the classical Cauchy problem of the generalized Maxwell field is well
posed and that the field possess the expected gauge invariance. Then the
classical phase space is developed in terms of gauge equivalent classes, first
in terms of the Cauchy data and then reformulated in terms of Maxwell
solutions. The latter is employed to quantize the field in the framework of
Dimock. Finally, the resulting algebra of observables is shown to satisfy the
wave equation with the usual canonical commutation relations.Comment: 17 pages, 1 figure, typset in RevTeX4. This version contains
substantial revisions in the discussion of the Cauchy problem for the
generalized Maxwell field equatio
Fourth order gravity: equations, history, and applications to cosmology
The field equations following from a Lagrangian L(R) will be deduced and
solved for special cases. If L is a non-linear function of the curvature
scalar, then these equations are of fourth order in the metric. In the
introduction we present the history of these equations beginning with the paper
of H. Weyl from 1918, who first discussed them as alternative to Einstein's
theory. In the third part, we give details about the cosmic no hair theorem,
i.e., the details how within fourth order gravity with L= R + R^2 the
inflationary phase of cosmic evolution turns out to be a transient attractor.
Finally, the Bicknell theorem, i.e. the conformal relation from fourth order
gravity to scalar-tensor theory, will be shortly presented.Comment: 51 pages, LaTeX, no figure, lecture for 42nd Karpacz Winter School
6.-11.2.06, references 99-109 and related comments are adde
Quadratic superconducting cosmic strings revisited
It has been shown that 5-dimensional general relativity action extended by
appropriate quadratic terms admits a singular superconducting cosmic string
solution. We search for cosmic strings endowed with similar and extended
physical properties by directly integrating the non-linear matrix field
equations thus avoiding the perturbative approach by which we constructed the
above-mentioned \textsl{exact} solution. The most general superconducting
cosmic string, subject to some constraints, will be derived and shown to be
mathematically \textsl{unique} up to linear coordinate transformations mixing
its Killing vectors. The most general solution, however, is not globally
equivalent to the old one due to the existence of Killing vectors with closed
orbits.Comment: 6 page
Some notes on the Kruskal - Szekeres completion
The Kruskal - Szekeres (KS) completion of the Schwarzschild spacetime is open
to Synge's methodological criticism that the KS procedure generates "good"
coordinates from "bad". This is addressed here in two ways: First I generate
the KS coordinates from Israel coordinates, which are also "good", and then I
generate the KS coordinates directly from a streamlined integration of the
Einstein equations.Comment: One typo correcte
Interior perfect fluid scalar-tensor solution
We present a new exact perfect fluid interior solution for a particular
scalar-tensor theory. The solution is regular everywhere and has a well defined
boundary where the fluid pressure vanishes. The metric and the dilaton field
match continuously the external solution.Comment: 8 pages, 3 figures, LaTe
Energy conditions in modified Gauss-Bonnet gravity
In considering alternative higher-order gravity theories, one is liable to be
motivated in pursuing models consistent and inspired by several candidates of a
fundamental theory of quantum gravity. Indeed, motivations from string/M-theory
predict that scalar field couplings with the Gauss-Bonnet invariant, G, are
important in the appearance of non-singular early time cosmologies. In this
work, we discuss the viability of an interesting alternative gravitational
theory, namely, modified Gauss-Bonnet gravity or f(G) gravity. We consider
specific realistic forms of f(G) analyzed in the literature that account for
the late-time cosmic acceleration and that have been found to cure the
finite-time future singularities present in the dark energy models. We present
the general inequalities imposed by the energy conditions and use the recent
estimated values of the Hubble, deceleration, jerk and snap parameters to
examine the viability of the above-mentioned forms of f(G) imposed by the weak
energy condition.Comment: 9 pages, 8 figures. V2: minor additions and corrections; to appear in
PR
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