123 research outputs found
Compact anisotropic spheres with prescribed energy density
New exact interior solutions to the Einstein field equations for anisotropic
spheres are found. We utilise a procedure that necessitates a choice for the
energy density and the radial pressure. This class contains the constant
density model of Maharaj and Maartens (Gen. Rel. Grav., Vol 21, 899-905, 1989)
and the variable density model of Gokhroo and Mehra (Gen. Rel. Grav., Vol 26,
75-84, 1994) as special cases. These anisotropic spheres match smoothly to the
Schwarzschild exterior and gravitational potentials are well behaved in the
interior. A graphical analysis of the matter variables is performed which
points to a physically reasonable matter distribution.Comment: 22 pages, 3 figures, to appear in Gen. Rel. Gra
Saccade frequency response to visual cues during gait in Parkinson's disease: the selective role of attention
Gait impairment is a core feature of Parkinson's disease (PD) with implications for falls risk. Visual cues improve gait in PD, but the underlying mechanisms are unclear. Evidence suggests that attention and vision play an important role; however, the relative contribution from each is unclear. Measurement of visual exploration (specifically saccade frequency) during gait allows for real-time measurement of attention and vision. Understanding how visual cues influence visual exploration may allow inferences of the underlying mechanisms to response which could help to develop effective therapeutics. This study aimed to examine saccade frequency during gait in response to a visual cue in PD and older adults and investigate the roles of attention and vision in visual cue response in PD. A mobile eye-tracker measured saccade frequency during gait in 55 people with PD and 32 age-matched controls. Participants walked in a straight line with and without a visual cue (50 cm transverse lines) presented under single task and dual-task (concurrent digit span recall). Saccade frequency was reduced when walking in PD compared to controls; however, visual cues ameliorated saccadic deficit. Visual cues significantly increased saccade frequency in both PD and controls under both single task and dual-task. Attention rather than visual function was central to saccade frequency and gait response to visual cues in PD. In conclusion, this study highlights the impact of visual cues on visual exploration when walking and the important role of attention in PD. Understanding these complex features will help inform intervention development
Conformally symmetric vacuum solutions of the gravitational field equations in the brane-world models
A class of exact solutions of the gravitational field equations in the vacuum
on the brane are obtained by assuming the existence of a conformal Killing
vector field, with non-static and non-central symmetry. In this case the
general solution of the field equations can be obtained in a parametric form in
terms of the Bessel functions. The behavior of the basic physical parameters
describing the non-local effects generated by the gravitational field of the
bulk (dark radiation and dark pressure) is also considered in detail, and the
equation of state satisfied at infinity by these quantities is derived. As a
physical application of the obtained solutions we consider the behavior of the
angular velocity of a test particle moving in a stable circular orbit. The
tangential velocity of the particle is a monotonically increasing function of
the radial distance and, in the limit of large values of the radial coordinate,
tends to a constant value, which is independent on the parameters describing
the model. Therefore a brane geometry admitting a one-parameter group of
conformal motions may provide an explanation for the dynamics of the neutral
hydrogen clouds at large distances from the galactic center, which is usually
explained by postulating the existence of the dark matter.Comment: 15 pages, 5 figures, to appear in Annals of Physic
Vacuum solutions of the gravitational field equations in the brane world model
We consider some classes of solutions of the static, spherically symmetric
gravitational field equations in the vacuum in the brane world scenario, in
which our Universe is a three-brane embedded in a higher dimensional
space-time. The vacuum field equations on the brane are reduced to a system of
two ordinary differential equations, which describe all the geometric
properties of the vacuum as functions of the dark pressure and dark radiation
terms (the projections of the Weyl curvature of the bulk, generating non-local
brane stresses). Several classes of exact solutions of the vacuum gravitational
field equations on the brane are derived. In the particular case of a vanishing
dark pressure the integration of the field equations can be reduced to the
integration of an Abel type equation. A perturbative procedure, based on the
iterative solution of an integral equation, is also developed for this case.
Brane vacuums with particular symmetries are investigated by using Lie group
techniques. In the case of a static vacuum brane admitting a one-parameter
group of conformal motions the exact solution of the field equations can be
found, with the functional form of the dark radiation and pressure terms
uniquely fixed by the symmetry. The requirement of the invariance of the field
equations with respect to the quasi-homologous group of transformations also
imposes a unique, linear proportionality relation between the dark energy and
dark pressure. A homology theorem for the static, spherically symmetric
gravitational field equations in the vacuum on the brane is also proven.Comment: 13 pages, no figures, to appear in PR
Absolute Stability Limit for Relativistic Charged Spheres
We find an exact solution for the stability limit of relativistic charged
spheres for the case of constant gravitational mass density and constant charge
density. We argue that this provides an absolute stability limit for any
relativistic charged sphere in which the gravitational mass density decreases
with radius and the charge density increases with radius. We then provide a
cruder absolute stability limit that applies to any charged sphere with a
spherically symmetric mass and charge distribution. We give numerical results
for all cases. In addition, we discuss the example of a neutral sphere
surrounded by a thin, charged shell.Comment: 25 pages, 1 figure 1 June 07: Replaced with added citations to prior
work along same line
Minimum mass-radius ratio for charged gravitational objects
We rigorously prove that for compact charged general relativistic objects
there is a lower bound for the mass-radius ratio. This result follows from the
same Buchdahl type inequality for charged objects, which has been extensively
used for the proof of the existence of an upper bound for the mass-radius
ratio. The effect of the vacuum energy (a cosmological constant) on the minimum
mass is also taken into account. Several bounds on the total charge, mass and
the vacuum energy for compact charged objects are obtained from the study of
the Ricci scalar invariants. The total energy (including the gravitational one)
and the stability of the objects with minimum mass-radius ratio is also
considered, leading to a representation of the mass and radius of the charged
objects with minimum mass-radius ratio in terms of the charge and vacuum energy
only.Comment: 19 pages, accepted by GRG, references corrected and adde
Sharp bounds on the critical stability radius for relativistic charged spheres
In a recent paper by Giuliani and Rothman \cite{GR}, the problem of finding a
lower bound on the radius of a charged sphere with mass M and charge Q<M is
addressed. Such a bound is referred to as the critical stability radius.
Equivalently, it can be formulated as the problem of finding an upper bound on
M for given radius and charge. This problem has resulted in a number of papers
in recent years but neither a transparent nor a general inequality similar to
the case without charge, i.e., M\leq 4R/9, has been found. In this paper we
derive the surprisingly transparent inequality
The
inequality is shown to hold for any solution which satisfies
where and are the radial- and tangential pressures respectively
and is the energy density. In addition we show that the inequality
is sharp, in particular we show that sharpness is attained by infinitely thin
shell solutions.Comment: 20 pages, 1 figur
Bianchi Type V Viscous Fluid Cosmological Models in Presence of Decaying Vacuum Energy
Bianchi type V viscous fluid cosmological model for barotropic fluid
distribution with varying cosmological term is investigated. We have
examined a cosmological scenario proposing a variation law for Hubble parameter
in the background of homogeneous, anisotropic Bianchi type V space-time.
The model isotropizes asymptotically and the presence of shear viscosity
accelerates the isotropization. The model describes a unified expansion history
of the universe indicating initial decelerating expansion and late time
accelerating phase. Cosmological consequences of the model are also discussed.Comment: 10 pages, 3 figure
A rotating three component perfect fluid source and its junction with empty space-time
The Kerr solution for empty space-time is presented in an ellipsoidally
symmetric coordinate system and it is used to produce generalised ellipsoidal
metrics appropriate for the generation of rotating interior solutions of
Einstein's equations. It is shown that these solutions are the familiar static
perfect fluid cases commonly derived in curvature coordinates but now endowed
with rotation. The resulting solutions are also discussed in the context of
T-solutions of Einstein's equations and the vacuum T-solution outside a
rotating source is presented. The interior source for these solutions is shown
not to be a perfect fluid but rather an anisotropic three component perfect
fluid for which the energy momentum tensor is derived. The Schwarzschild
interior solution is given as an example of the approach.Comment: 14 page
Strange stars in Krori-Barua space-time
The singularity space-time metric obtained by Krori and Barua\cite{Krori1975}
satisfies the physical requirements of a realistic star. Consequently, we
explore the possibility of applying the Krori and Barua model to describe
ultra-compact objects like strange stars. For it to become a viable model for
strange stars, bounds on the model parameters have been obtained. Consequences
of a mathematical description to model strange stars have been analyzed.Comment: 9 pages (two column), 12 figures. Some changes have been made. " To
appear in European Physical Journal C
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