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 $$\begin{split} &\partial \psi_{1} = (|\psi_{1}|^{2} + |\psi_{2}|^{2}) \psi_{2} \\ &\bar{\partial} \psi_{2} =- (|\psi_{1}|^{2} + |\psi_{2}|^{2}) \psi_{1} \end{split}$$ 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 $S^{2} \subset E^{3}$

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 $\psi_0$ 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 $\psi_0$. 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 $g_{c}\simeq 4.8\times 10^{31}m/s^{2}$ and $g_{c}\simeq 8.8\times 10^{34}m/s^{2}$, 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 $R_{\overline{p} p/ p p}$ at CM angle $\theta = 90^0$ 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 $R_{np/pp}$ is also discussed.Comment: 18 pages, latex2e, 4 uuencoded figures, include