678 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.
On the black hole limit of rotating discs and rings
Solutions to Einstein's field equations describing rotating fluid bodies in
equilibrium permit parametric (i.e. quasi-stationary) transitions to the
extreme Kerr solution (outside the horizon). This has been shown analytically
for discs of dust and numerically for ring solutions with various equations of
state. From the exterior point of view, this transition can be interpreted as a
(quasi) black hole limit. All gravitational multipole moments assume precisely
the values of an extremal Kerr black hole in the limit. In the present paper,
the way in which the black hole limit is approached is investigated in more
detail by means of a parametric Taylor series expansion of the exact solution
describing a rigidly rotating disc of dust. Combined with numerical
calculations for ring solutions our results indicate an interesting universal
behaviour of the multipole moments near the black hole limit.Comment: 18 pages, 4 figures; Dedicated to Gernot Neugebauer on the occasion
of his 70th birthda
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
General relativistic gravitational field of a rigidly rotating disk of dust: Solution in terms of ultraelliptic functions
In a recent paper we presented analytic expressions for the axis potential,
the disk metric, and the surface mass density of the global solution to
Einstein's field equations describing a rigidly rotating disk of dust. Here we
add the complete solution in terms of ultraelliptic functions and quadratures.Comment: 5 pages, published in 1995 [Phys. Rev. Lett. 75 (1995) 3046
Hadrons and Nuclei
This document is one of a series of whitepapers from the USQCD collaboration.
Here, we discuss opportunities for lattice QCD calculations related to the
structure and spectroscopy of hadrons and nuclei. An overview of recent lattice
calculations of the structure of the proton and other hadrons is presented
along with prospects for future extensions. Progress and prospects of hadronic
spectroscopy and the study of resonances in the light, strange and heavy quark
sectors is summarized. Finally, recent advances in the study of light nuclei
from lattice QCD are addressed, and the scope of future investigations that are
currently envisioned is outlined.Comment: 45 page
The Ernst equation and ergosurfaces
We show that analytic solutions \mcE of the Ernst equation with non-empty
zero-level-set of \Re \mcE lead to smooth ergosurfaces in space-time. In
fact, the space-time metric is smooth near a "Ernst ergosurface" if and
only if \mcE is smooth near and does not have zeros of infinite order
there.Comment: 23 pages, 4 figures; misprints correcte
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
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