280 research outputs found
The Post-Newtonian Approximation of the Rigidly Rotating Disc of Dust to Arbitrary Order
Using the analytic, global solution for the rigidly rotating disc of dust as
a starting point, an iteration scheme is presented for the calculation of an
arbitrary coefficient in the post-Newtonian (PN) approximation of this
solution. The coefficients were explicitly calculated up to the 12th PN level
and are listed in this paper up to the 4th PN level. The convergence of the
series is discussed and the approximation is found to be reliable even in
highly relativistic cases. Finally, the ergospheres are calculated at
increasing orders of the approximation and for increasingly relativistic
situations.Comment: 19 pages, 2 tables, 4 figures Accepted for publication in Phys. Rev.
Differentially rotating disks of dust
We present a three-parameter family of solutions to the stationary
axisymmetric Einstein equations that describe differentially rotating disks of
dust. They have been constructed by generalizing the Neugebauer-Meinel solution
of the problem of a rigidly rotating disk of dust. The solutions correspond to
disks with angular velocities depending monotonically on the radial coordinate;
both decreasing and increasing behaviour is exhibited. In general, the
solutions are related mathematically to Jacobi's inversion problem and can be
expressed in terms of Riemann theta functions. A particularly interesting
two-parameter subfamily represents Baecklund transformations to appropriate
seed solutions of the Weyl class.Comment: 14 pages, 3 figures. To appear in "General Relativity and
Gravitation". Second version with minor correction
Dirichlet Boundary Value Problems of the Ernst Equation
We demonstrate how the solution to an exterior Dirichlet boundary value
problem of the axisymmetric, stationary Einstein equations can be found in
terms of generalized solutions of the Backlund type. The proof that this
generalization procedure is valid is given, which also proves conjectures about
earlier representations of the gravitational field corresponding to rotating
disks of dust in terms of Backlund type solutions.Comment: 22 pages, to appear in Phys. Rev. D, Correction of a misprint in
equation (4
Monodromy transform and the integral equation method for solving the string gravity and supergravity equations in four and higher dimensions
The monodromy transform and corresponding integral equation method described
here give rise to a general systematic approach for solving integrable
reductions of field equations for gravity coupled bosonic dynamics in string
gravity and supergravity in four and higher dimensions. For different types of
fields in space-times of dimensions with commuting isometries
-- stationary fields with spatial symmetries, interacting waves or partially
inhomogeneous cosmological models, the string gravity equations govern the
dynamics of interacting gravitational, dilaton, antisymmetric tensor and any
number of Abelian vector gauge fields (all depending only on two
coordinates). The equivalent spectral problem constructed earlier allows to
parameterize the infinite-dimensional space of local solutions of these
equations by two pairs of \cal{arbitrary} coordinate-independent holomorphic
- and - matrix functions of a spectral parameter which constitute a complete set
of monodromy data for normalized fundamental solution of this spectral problem.
The "direct" and "inverse" problems of such monodromy transform --- calculating
the monodromy data for any local solution and constructing the field
configurations for any chosen monodromy data always admit unique solutions. We
construct the linear singular integral equations which solve the inverse
problem. For any \emph{rational} and \emph{analytically matched} (i.e.
and
) monodromy data the solution for string
gravity equations can be found explicitly. Simple reductions of the space of
monodromy data leads to the similar constructions for solving of other
integrable symmetry reduced gravity models, e.g. 5D minimal supergravity or
vacuum gravity in dimensions.Comment: RevTex 7 pages, 1 figur
Differentially rotating disks of dust: Arbitrary rotation law
In this paper, solutions to the Ernst equation are investigated that depend
on two real analytic functions defined on the interval [0,1]. These solutions
are introduced by a suitable limiting process of Backlund transformations
applied to seed solutions of the Weyl class. It turns out that this class of
solutions contains the general relativistic gravitational field of an arbitrary
differentially rotating disk of dust, for which a continuous transition to some
Newtonian disk exists. It will be shown how for given boundary conditions (i.
e. proper surface mass density or angular velocity of the disk) the
gravitational field can be approximated in terms of the above solutions.
Furthermore, particular examples will be discussed, including disks with a
realistic profile for the angular velocity and more exotic disks possessing two
spatially separated ergoregions.Comment: 23 pages, 3 figures, submitted to 'General Relativity and
Gravitation
Analytical approximation of the exterior gravitational field of rotating neutron stars
It is known that B\"acklund transformations can be used to generate
stationary axisymmetric solutions of Einstein's vacuum field equations with any
number of constants. We will use this class of exact solutions to describe the
exterior vacuum region of numerically calculated neutron stars. Therefore we
study how an Ernst potential given on the rotation axis and containing an
arbitrary number of constants can be used to determine the metric everywhere.
Then we review two methods to determine those constants from a numerically
calculated solution. Finally, we compare the metric and physical properties of
our analytic solution with the numerical data and find excellent agreement even
for a small number of parameters.Comment: 9 pages, 10 figures, 3 table
Dynamics of charged fluids and 1/L perturbation expansions
Some features of the calculation of fluid dynamo systems in
magnetohydrodynamics are studied. In the coupled set of the ordinary linear
differential equations for the spherically symmetric dynamos, the
problem represented by the presence of the mixed (Robin) boundary conditions is
addressed and a new treatment for it is proposed. The perturbation formalism of
large expansions is shown applicable and its main technical steps are
outlined.Comment: 16 p
Approaches to the Monopole-Dynamic Dipole Vacuum Solution Concerning the Structure of its Ernst's Potential on the Symmetry Axis
The FHP algorithm allows to obtain the relativistic multipole moments of a
vacuum stationary axisymmetric solution in terms of coefficients which appear
in the expansion of its Ernst's potential on the symmetry axis. First of all,
we will use this result in order to determine, at a certain approximation
degree, the Ernst's potential on the symmetry axis of the metric whose only
multipole moments are mass and angular momentum.
By using Sibgatullin's method we analyse a series of exacts solutions with
the afore mentioned multipole characteristic. Besides, we present an
approximate solution whose Ernst's potential is introduced as a power series of
a dimensionless parameter. The calculation of its multipole moments allows us
to understand the existing differences between both approximations to the
proposed pure multipole solution.Comment: 24 pages, plain TeX. To be published in General Relativity and
Gravitatio
Diagnosing and mapping pulmonary emphysema on X-ray projection images
To assess whether grating-based X-ray dark-field imaging can increase the sensitivity of X-ray projection images in the diagnosis of pulmonary emphysema and allow for a more accurate assessment of emphysema distribution. Lungs from three mice with pulmonary emphysema and three healthy mice were imaged ex vivo using a laser-driven compact synchrotron X-ray source. Median signal intensities of transmission (T), dark-field (V) and a combined parameter (normalized scatter) were compared between emphysema and control group. To determine the diagnostic value of each parameter in differentiating between healthy and emphysematous lung tissue, a receiver-operating-characteristic (ROC) curve analysis was performed both on a per-pixel and a per-individual basis. Parametric maps of emphysema distribution were generated using transmission, dark-field and normalized scatter signal and correlated with histopathology. Transmission values relative to water were higher for emphysematous lungs than for control lungs (1.11 vs. 1.06, p<0.001). There was no difference in median dark-field signal intensities between both groups (0.66 vs. 0.66). Median normalized scatter was significantly lower in the emphysematous lungs compared to controls (4.9 vs. 10.8, p<0.001), and was the best parameter for differentiation of healthy vs. emphysematous lung tissue. In a per-pixel analysis, the area under the ROC curve (AUC) for the normalized scatter value was significantly higher than for transmission (0.86 vs. 0.78, p<0.001) and dark-field value (0.86 vs. 0.52, p<0.001) alone. Normalized scatter showed very high sensitivity for a wide range of specificity values (94% sensitivity at 75% specificity). Using the normalized scatter signal to display the regional distribution of emphysema provides color-coded parametric maps, which show the best correlation with histopathology. In a murine model, the complementary information provided by X-ray transmission and dark-field images adds incremental diagnostic value in detecting pulmonary emphysema and visualizing its regional distribution as compared to conventional X-ray projections
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