782 research outputs found
Scalar--flat K\"ahler metrics with conformal Bianchi V symmetry
We provide an affirmative answer to a question posed by Tod \cite{Tod:1995b},
and construct all four-dimensional Kahler metrics with vanishing scalar
curvature which are invariant under the conformal action of Bianchi V group.
The construction is based on the combination of twistor theory and the
isomonodromic problem with two double poles. The resulting metrics are
non-diagonal in the left-invariant basis and are explicitly given in terms of
Bessel functions and their integrals. We also make a connection with the LeBrun
ansatz, and characterise the associated solutions of the SU(\infty) Toda
equation by the existence a non-abelian two-dimensional group of point
symmetries.Comment: Dedicated to Maciej Przanowski on the occasion of his 65th birthday.
Minor corrections. To appear in CQ
Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis
We investigate the relaxation dynamics of the integrable Lieb-Liniger model
of contact-interacting bosons in one dimension following a sudden quench of the
collisional interaction strength. The system is initially prepared in its
noninteracting ground state and the interaction strength is then abruptly
switched to a positive value, corresponding to repulsive interactions between
the bosons. We calculate equal-time correlation functions of the nonequilibrium
Bose field for small systems of up to five particles via symbolic evaluation of
coordinate Bethe-ansatz expressions for operator matrix elements between
Lieb-Liniger eigenstates. We characterize the relaxation of the system by
comparing the time-evolving correlation functions following the quench to the
equilibrium correlations predicted by the diagonal ensemble and relate the
behavior of these correlations to that of the quantum fidelity between the
many-body wave function and the initial state of the system. Our results for
the asymptotic scaling of local second-order correlations with increasing
interaction strength agree with the predictions of recent generalized
thermodynamic Bethe-ansatz calculations. By contrast, third-order correlations
obtained within our approach exhibit a markedly different power-law dependence
on the interaction strength as the Tonks-Girardeau limit of infinitely strong
interactions is approached.Comment: 19 pages, 10 figures. v3: Final version. Typos fixed, and other minor
change
Matching of spatially homogeneous non-stationary space--times to vacuum in cylindrical symmetry
We study the matching of LRS spatially homogeneous collapsing dust
space-times with non-stationary vacuum exteriors in cylindrical symmetry. Given
an interior with diagonal metric we prove existence and uniqueness results for
the exterior. The matched solutions contain trapped surfaces, singularities and
Cauchy horizons. The solutions cannot be asymptotically flat and we present
evidence that they are singular on the Cauchy horizons.Comment: LaTeX, 15 pages, 1 figure, submitted for publicatio
Complete Calabi-Yau metrics from Kahler metrics in D=4
In the present work the local form of certain Calabi-Yau metrics possessing a
local Hamiltonian Killing vector is described in terms of a single non linear
equation. The main assumptions are that the complex -form is of the form
, where is preserved by the Killing
vector, and that the space of the orbits of the Killing vector is, for fixed
value of the momentum map coordinate, a complex 4-manifold, in such a way that
the complex structure of the 4-manifold is part of the complex structure of the
complex 3-fold. The link with the solution generating techniques of [26]-[28]
is made explicit and in particular an example with holonomy exactly SU(3) is
found by use of the linearization of [26], which was found in the context of D6
branes wrapping a holomorphic 1-fold in a hyperkahler manifold. But the main
improvement of the present method, unlike the ones presented in [26]-[28], does
not rely in an initial hyperkahler structure. Additionally the complications
when dealing with non linear operators over the curved hyperkahler space are
avoided by use of this method.Comment: Version accepted for publication in Phys.Rev.
“It’s my dream to work with Olympic athletes”: Neophyte sport psychologists’ expectations and initial experiences regarding service delivery
We examined trainee practitioners' initial experiences of applied sport psychology practice. Semi-structured interviews (4) were conducted over 6 months with 7 full-time MSc students before, during, and after the applied sport psychology module, when they were working with clients. Participants also kept reflective diaries over an 8-week period whilst working with clients. Findings included: (a) motivations and expectations of an ASP practice career, (b) perceptions of service delivery, (c) emotional demands, and (d) pivotal experiences. Findings extend previous literature on the initial stages of practitioner development, providing micro-level detail on aspects of the intense development process during this pivotal perio
Discovery of a 6.4 keV Emission Line in a Burst from SGR 1900+14
We present evidence of a 6.4 keV emission line during a burst from the soft
gamma-ray repeater SGR 1900+14. The Rossi X-ray Timing Explorer (RXTE)
monitored this source extensively during its outburst in the summer of 1998. A
strong burst observed on August 29, 1998 revealed a number of unique
properties. The burst exhibits a precursor and is followed by a long (~ 1000 s)
tail modulated at the 5.16 s stellar rotation period. The precursor has a
duration of 0.85 s and shows both significant spectral evolution as well as an
emission feature centered near 6.4 keV during the first 0.3 s of the event,
when the X-ray spectrum was hardest. The continuum during the burst is well fit
with an optically thin thermal bremsstrahlung (OTTB) spectrum with the
temperature ranging from about 40 to 10 keV. The line is strong, with an
equivalent width of 400 eV, and is consistent with Fe K-alpha fluorescence from
relatively cool material. If the rest-frame energy is indeed 6.4 keV, then the
lack of an observed redshift indicates that the source is at least 80 km above
the neutron star surface. We discuss the implications of the line detection in
the context of models for SGRs.Comment: AASTex preprint, 14 pages, 3 embedded figures. Accepted for
Publication in Astrophysical Journal Letter
A note on behaviour at an isotropic singularity
The behaviour of Jacobi fields along a time-like geodesic running into an
isotropic singularity is studied. It is shown that the Jacobi fields are
crushed to zero length at a rate which is the same in every direction
orthogonal to the geodesic. We show by means of a counter-example that this
crushing effect depends crucially on a technicality of the definition of
isotropic singularities, and not just on the uniform degeneracy of the metric
at the singularity.Comment: 13 pp. plain latex. To appear in Classical and Quantum Gravit
Bianchi type II,III and V diagonal Einstein metrics re-visited
We present, for both minkowskian and euclidean signatures, short derivations
of the diagonal Einstein metrics for Bianchi type II, III and V. For the first
two cases we show the integrability of the geodesic flow while for the third
case a somewhat unusual bifurcation phenomenon takes place: for minkowskian
signature elliptic functions are essential in the metric while for euclidean
signature only elementary functions appear
The Dynamics of a Classical Spinning Particle in Vaidya Space-Time
Based on the Mathisson-Papapetrou-Dixon (MPD) equations and the Vaidya
metric, the motion of a spinning point particle orbiting a non-rotating star
while undergoing radiation-induced gravitational collapse is studied in detail.
A comprehensive analysis of the orbital dynamics is performed assuming distinct
central mass functions which satisfy the weak energy condition, in order to
determine a correspondence between the choice of mass function and the spinning
particle's orbital response, as reflected in the gravitational waves emitted by
the particle. The analysis presented here is likely most beneficial for the
observation of rotating solar mass black holes or neutron stars in orbit around
intermediate-sized Schwarzschild black holes undergoing radiation collapse. The
possibility of detecting the effects of realistic mass accretion based on this
approach is considered. While it seems unlikely to observe such effects based
on present technology, they may perhaps become observable with the advent of
future detectors.Comment: REVTeX file, 20 pages, 26 figure
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