614 research outputs found
Links between different analytic descriptions of constant mean curvature surfaces
Transformations between different analytic descriptions of constant mean
curvature (CMC) surfaces are established. In particular, it is demonstrated
that the system descriptive of CMC surfaces within the
framework of the generalized Weierstrass representation, decouples into a
direct sum of the elliptic Sh-Gordon and Laplace equations. Connections of this
system with the sigma model equations are established. It is pointed out, that
the instanton solutions correspond to different Weierstrass parametrizations of
the standard sphere
Metric of a tidally perturbed spinning black hole
We explicitly construct the metric of a Kerr black hole that is tidally
perturbed by the external universe in the slow-motion approximation. This
approximation assumes that the external universe changes slowly relative to the
rotation rate of the hole, thus allowing the parameterization of the
Newman-Penrose scalar by time-dependent electric and magnetic tidal
tensors. This approximation, however, does not constrain how big the spin of
the background hole can be and, in principle, the perturbed metric can model
rapidly spinning holes. We first generate a potential by acting with a
differential operator on . From this potential we arrive at the metric
perturbation by use of the Chrzanowski procedure in the ingoing radiation
gauge. We provide explicit analytic formulae for this metric perturbation in
spherical Kerr-Schild coordinates, where the perturbation is finite at the
horizon. This perturbation is parametrized by the mass and Kerr spin parameter
of the background hole together with the electric and magnetic tidal tensors
that describe the time evolution of the perturbation produced by the external
universe. In order to take the metric accurate far away from the hole, these
tidal tensors should be determined by asymptotically matching this metric to
another one valid far from the hole. The tidally perturbed metric constructed
here could be useful in initial data constructions to describe the metric near
the horizons of a binary system of spinning holes. This perturbed metric could
also be used to construct waveforms and study the absorption of mass and
angular momentum by a Kerr black hole when external processes generate
gravitational radiation.Comment: 17 pages, 3 figures. Final PRD version, minor typos, etc corrected.
v3: corrected typo in Eq. (35) and (57
Gravitational collapse in asymptotically Anti-de Sitter/de Sitter backgrounds
We study here the gravitational collapse of a matter cloud with a
non-vanishing tangential pressure in the presence of a non-zero cosmological
term. Conditions for bounce and singularity formation are derived for the
model. It is also shown that when the tangential pressures vanish, the bounce
and singularity conditions reduce to that of the dust case studied earlier. The
collapsing interior is matched with an exterior which is asymptotically de
Sitter or anti de Sitter, depending on the sign of cosmological constant. The
junction conditions for matching the cloud to exterior are specified. The
effect of the cosmological term on apparent horizons is studied in some detail,
and the nature of central singularity is analyzed. We also discuss here the
visibility of the singularity and implications for the cosmic censorship
conjecture.Comment: 11 pages, 1 figure, Revtex
The optical system of the H.E.S.S. imaging atmospheric Cherenkov telescopes, Part II: mirror alignment and point spread function
Mirror facets of the H.E.S.S. imaging atmospheric Cherenkov telescopes are
aligned using stars imaged onto the closed lid of the PMT camera, viewed by a
CCD camera. The alignment procedure works reliably and includes the automatic
analysis of CCD images and control of the facet alignment actuators. On-axis,
80% of the reflected light is contained in a circle of less than 1 mrad
diameter. The spot widens with increasing angle to the telescope axis. In
accordance with simulations, the spot size has roughly doubled at an angle of
1.4 degr. from the axis. The expected variation of spot size with elevation due
to deformations of the support structure is visible, but is completely
non-critical over the usual working range. Overall, the optical quality of the
telescope exceeds the specifications.Comment: 23 pages, 13 figure
de Sitter special relativity
A special relativity based on the de Sitter group is introduced, which is the
theory that might hold up in the presence of a non-vanishing cosmological
constant. Like ordinary special relativity, it retains the quotient character
of spacetime, and a notion of homogeneity. As a consequence, the underlying
spacetime will be a de Sitter spacetime, whose associated kinematics will
differ from that of ordinary special relativity. The corresponding modified
notions of energy and momentum are obtained, and the exact relationship between
them, which is invariant under a re-scaling of the involved quantities,
explicitly exhibited. Since the de Sitter group can be considered a particular
deformation of the Poincar\'e group, this theory turns out to be a specific
kind of deformed (or doubly) special relativity. Some experimental
consequences, as well as the causal structure of spacetime--modified by the
presence of the de Sitter horizon--are briefly discussed.Comment: V2: Some presentation changes; a new section introduced, with a
discussion about possible phenomenological consequences; new references
added; version to be published in Classical and Quantum Gravit
On the equivalence principle and gravitational and inertial mass relation of classical charged particles
We show that the locally constant force necessary to get a stable hyperbolic
motion regime for classical charged point particles, actually, is a combination
of an applied external force and of the electromagnetic radiation reaction
force. It implies, as the strong Equivalence Principle is valid, that the
passive gravitational mass of a charged point particle should be slight greater
than its inertial mass. An interesting new feature that emerges from the
unexpected behavior of the gravitational and inertial mass relation, for
classical charged particles, at very strong gravitational field, is the
existence of a critical, particle dependent, gravitational field value that
signs the validity domain of the strong Equivalence Principle. For electron and
proton, these critical field values are
and , respectively
From wormhole to time machine: Comments on Hawking's Chronology Protection Conjecture
The recent interest in ``time machines'' has been largely fueled by the
apparent ease with which such systems may be formed in general relativity,
given relatively benign initial conditions such as the existence of traversable
wormholes or of infinite cosmic strings. This rather disturbing state of
affairs has led Hawking to formulate his Chronology Protection Conjecture,
whereby the formation of ``time machines'' is forbidden. This paper will use
several simple examples to argue that the universe appears to exhibit a
``defense in depth'' strategy in this regard. For appropriate parameter regimes
Casimir effects, wormhole disruption effects, and gravitational back reaction
effects all contribute to the fight against time travel. Particular attention
is paid to the role of the quantum gravity cutoff. For the class of model
problems considered it is shown that the gravitational back reaction becomes
large before the Planck scale quantum gravity cutoff is reached, thus
supporting Hawking's conjecture.Comment: 43 pages,ReV_TeX,major revision
On the K^+D Interaction at Low Energies
The Kd reactions are considered in the impulse approximation with NN
final-state interactions (NN FSI) taken into account. The realistic parameters
for the KN phase shifts are used. The "quasi-elastic" energy region, in which
the elementary KN interaction is predominantly elastic, is considered. The
theoretical predictions are compared with the data on the K^+d->K^+pn,
K^+d->K^0pp, K^+d->K^+d and K^+d total cross sections. The NN FSI effect in the
reaction K^+d->K^+pn has been found to be large. The predictions for the Kd
cross sections are also given for slow kaons, produced from phi(1020) decays,
as the functions of the isoscalar KN scattering length a_0. These predictions
can be used to extract the value of a_0 from the data.Comment: 22 pages, 5 figure
The supersymmetric modified Poschl-Teller and delta-well potentials
New supersymmetric partners of the modified Poschl-Teller and the Dirac's
delta well potentials are constructed in closed form. The resulting
one-parametric potentials are shown to be interrelated by a limiting process.
The range of values of the parameters for which these potentials are free of
singularities is exactly determined. The construction of higher order
supersymmetric partner potentials is also investigated.Comment: 20 pages, LaTeX file, 4 eps figure
Wide-angle elastic scattering and color randomization
Baryon-baryon elastic scattering is considered in the independent scattering
(Landshoff) mechanism. It is suggested that for scattering at moderate
energies, direct and interchange quark channels contribute with equal color
coefficients because the quark color is randomized by soft gluon exchange
during the hadronization stage. With this assumption, it is shown that the
ratio of cross sections at CM angle
decreases from a high energy value of R_{\pbar p / pp} \approx 1/2.7, down to
R_{\pbar p / pp} \approx 1/28, compatible with experimental data at moderate
energies. This sizable fall in the ratio seems to be characteristic of the
Landshoff mechanism, in which changes at the quark level have a strong effect
precisely because the hadronic process occurs via multiple quark scatterings.
The effect of color randomization on the angular distribution of proton-proton
elastic scattering and the cross section ratio is also discussed.Comment: 18 pages, latex2e, 4 uuencoded figures, include
- …