886 research outputs found
Compensation for Primary Reflector Wavefront Error
The object of the invention is to compensate for errors in a large telescope primary reflector by making certain compensating deviations in a smaller, auxiliary reflector of the telescope. At least one intermediate element forms an image of the primary surface onto the secondary surface, so each point on the secondary surface corresponds to a point on the primary surface. The secondary surface is formed with a deviation from an ideal secondary surface, with the piston distance of each point on the actual secondary surface equal to the piston distance of a corresponding piston on the actual primary surface from the ideal primary surface. It is found that this results in electromagnetic (e.g., light) rays which strike a deviating area of the actual primary surface being brought to the same focus as if the actual primary surface did not have a diviation from an ideal primary surface
Highly accurate calculation of rotating neutron stars: Detailed description of the numerical methods
We give a detailed description of the recently developed multi-domain
spectral method for constructing highly accurate general-relativistic models of
rapidly rotating stars. For both "ordinary" and "critical" configurations, it
is exhibited by means of representative examples, how the accuracy improves as
the order of the approximation increases. Apart from homogeneous fluid bodies,
we also discuss models of polytropic and strange stars.Comment: 22 pages, 4 figures, 9 tables, version accepted by A&
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.
A classification (uniqueness) theorem for rotating black holes in 4D Einstein-Maxwell-dilaton theory
In the present paper we prove a classification (uniqueness) theorem for
stationary, asymptotically flat black hole spacetimes with connected and
non-degenerate horizon in 4D Einstein-Maxwell-dilaton theory with an arbitrary
dilaton coupling parameter . We show that such black holes are uniquely
specified by the length of the horizon interval, angular momentum, electric and
magnetic charge and the value of the dilaton field at infinity when the dilaton
coupling parameter satisfies . The proof is based on the
nonpositivity of the Riemann curvature operator on the space of the potentials.
A generalization of the classification theorem for spacetimes with disconnected
horizons is also given.Comment: 15 pages, v2 typos correcte
Bottomonium spectrum at order v^6 from domain-wall lattice QCD: precise results for hyperfine splittings
The bottomonium spectrum is computed in dynamical 2+1 flavor lattice QCD,
using NRQCD for the b quarks. The main calculations in this work are based on
gauge field ensembles generated by the RBC and UKQCD collaborations with the
Iwasaki action for the gluons and a domain-wall action for the sea quarks.
Lattice spacing values of approximately 0.08 fm and 0.11 fm are used, and
simultaneous chiral extrapolations to the physical pion mass are performed. As
a test for gluon discretization errors, the calculations are repeated on two
ensembles generated by the MILC collaboration with the Luscher-Weisz gauge
action. Gluon discretization errors are also studied in a lattice potential
model using perturbation theory for four different gauge actions. The
nonperturbative lattice QCD results for the radial and orbital bottomonium
energy splittings obtained from the RBC/UKQCD ensembles are found to be in
excellent agreement with experiment. To get accurate results for spin
splittings, the spin-dependent order-v^6 terms are included in the NRQCD
action, and suitable ratios are calculated such that most of the unknown
radiative corrections cancel. The cancellation of radiative corrections is
verified explicitly by repeating the calculations with different values of the
couplings in the NRQCD action. Using the lattice ratios of the S-wave hyperfine
and the 1P tensor splitting, and the experimental result for the 1P tensor
splitting, the 1S hyperfine splitting is found to be
60.3+-5.5(stat)+-5.0(syst)+-2.1(exp) MeV, and the 2S hyperfine splitting is
predicted to be 23.5+-4.1(stat)+-2.1(syst)+-0.8(exp) MeV.Comment: 36 pages, 14 figures. v2: added Appendix D containing detailed
analysis of gluon discretization errors using a lattice potential model and
comparison to results from MILC ensembles. Estimates of systematic errors in
hyperfine splittings now include gluon discretization errors and b-bbar
annihilation contribution. Accepted for publication in PR
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
The bottomonium spectrum from lattice QCD with 2+1 flavors of domain wall fermions
Recently, realistic lattice QCD calculations with 2+1 flavors of domain wall
fermions and the Iwasaki gauge action have been performed by the RBC and UKQCD
collaborations. Here, results for the bottomonium spectrum computed on their
gauge configurations of size 24^3x64 with a lattice spacing of approximately
0.11 fm and four different values for the light quark mass are presented.
Improved lattice NRQCD is used to treat the b quarks inside the bottomonium.
The results for the radial and orbital energy splittings are found to be in
good agreement with experimental measurements, indicating that systematic
errors are small. The calculation of the Upsilon(2S)-Upsilon(1S) energy
splitting provides an independent determination of the lattice spacing. For the
most physical ensemble it is found to be a^{-1}=1.740(25)(19) GeV, where the
first error is statistical/fitting and the second error is an estimate of the
systematic errors due to the lattice NRQCD action.Comment: 11 pages, 5 figures, added section on "speed of light"; to appear in
Phys. Rev.
Equilibrium Configurations of Homogeneous Fluids in General Relativity
By means of a highly accurate, multi-domain, pseudo-spectral method, we
investigate the solution space of uniformly rotating, homogeneous and
axisymmetric relativistic fluid bodies. It turns out that this space can be
divided up into classes of solutions. In this paper, we present two new classes
including relativistic core-ring and two-ring solutions. Combining our
knowledge of the first four classes with post-Newtonian results and the
Newtonian portion of the first ten classes, we present the qualitative
behaviour of the entire relativistic solution space. The Newtonian disc limit
can only be reached by going through infinitely many of the aforementioned
classes. Only once this limiting process has been consummated, can one proceed
again into the relativistic regime and arrive at the analytically known
relativistic disc of dust.Comment: 8 pages, colour figures, v3: minor additions including one reference,
accepted by MNRA
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
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