Scale invariance and critical gravitational collapse

We examine ways to write the Choptuik critical solution as the evolution of scale invariant variables. It is shown that a system of scale invariant variables proposed by one of the authors does not evolve periodically in the Choptuik critical solution. We find a different system, based on maximal slicing. This system does evolve periodically, and may generalize to the case of axisymmetry or of no symmetry at all.Comment: 7 pages, 3 figures, Revtex, discussion modified to clarify presentatio

Evolution equations for slowly rotating stars

We present a hyperbolic formulation of the evolution equations describing non-radial perturbations of slowly rotating relativistic stars in the Regge--Wheeler gauge. We demonstrate the stability preperties of the new evolution set of equations and compute the polar w-modes for slowly rotating stars.Comment: 27 pages, 2 figure

The naked singularity in the global structure of critical collapse spacetimes

We examine the global structure of scalar field critical collapse spacetimes using a characteristic double-null code. It can integrate past the horizon without any coordinate problems, due to the careful choice of constraint equations used in the evolution. The limiting sequence of sub- and supercritical spacetimes presents an apparent paradox in the expected Penrose diagrams, which we address in this paper. We argue that the limiting spacetime converges pointwise to a unique limit for all r>0, but not uniformly. The r=0 line is different in the two limits. We interpret that the two different Penrose diagrams differ by a discontinuous gauge transformation. We conclude that the limiting spacetime possesses a singular event, with a future removable naked singularity.Comment: RevTeX 4; 6 pages, 7 figure

Evidence of Water-related Discrete Trap State Formation in Pentacene Single Crystal Field-Effect Transistors

We report on the generation of a discrete trap state during negative gate bias stress in pentacene single crystal "flip-crystal" field-effect transistors with a SiO2 gate dielectric. Trap densities of up to 2*10^12 cm^-2 were created in the experiments. Trap formation and trap relaxation are distinctly different above and below ~280 K. In devices in which a self-assembled monolayer on top of the SiO2 provides a hydrophobic insulator surface we do not observe trap formation. These results indicate the microscopic cause of the trap state to be water adsorbed on the SiO2 surface.Comment: 13 pages, 4 figures, submitted to Applied Physics Letter

Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale

We conducted three torsion-balance experiments to test the gravitational inverse-square law at separations between 9.53 mm and 55 micrometers, probing distances less than the dark-energy length scale $\lambda_{\rm d}=\sqrt[4]{\hbar c/\rho_{\rm d}}\approx 85 \mu$m. We find with 95% confidence that the inverse-square law holds ($|\alpha| \leq 1$) down to a length scale $\lambda = 56 \mu$m and that an extra dimension must have a size $R \leq 44 \mu$m.Comment: 4 pages, 6 figure

Scalar field collapse in three-dimensional AdS spacetime

We describe results of a numerical calculation of circularly symmetric scalar field collapse in three spacetime dimensions with negative cosmological constant. The procedure uses a double null formulation of the Einstein-scalar equations. We see evidence of black hole formation on first implosion of a scalar pulse if the initial pulse amplitude $A$ is greater than a critical value $A_*$. Sufficiently near criticality the apparent horizon radius $r_{AH}$ grows with pulse amplitude according to the formula $r_{AH} \sim (A-A_*)^{0.81}$.Comment: 10 pages, 1 figure; references added, to appear in CQG(L

Density of bulk trap states in organic semiconductor crystals: discrete levels induced by oxygen in rubrene

The density of trap states in the bandgap of semiconducting organic single crystals has been measured quantitatively and with high energy resolution by means of the experimental method of temperature-dependent space-charge-limited-current spectroscopy (TD-SCLC). This spectroscopy has been applied to study bulk rubrene single crystals, which are shown by this technique to be of high chemical and structural quality. A density of deep trap states as low as ~ 10^{15} cm^{-3} is measured in the purest crystals, and the exponentially varying shallow trap density near the band edge could be identified (1 decade in the density of states per ~25 meV). Furthermore, we have induced and spectroscopically identified an oxygen related sharp hole bulk trap state at 0.27 eV above the valence band.Comment: published in Phys. Rev. B, high quality figures: http://www.cpfs.mpg.de/~krellner

Late-time evolution of nonlinear gravitational collapse

We study numerically the fully nonlinear gravitational collapse of a self-gravitating, minimally-coupled, massless scalar field in spherical symmetry. Our numerical code is based on double-null coordinates and on free evolution of the metric functions: The evolution equations are integrated numerically, whereas the constraint equations are only monitored. The numerical code is stable (unlike recent claims) and second-order accurate. We use this code to study the late-time asymptotic behavior at fixed $r$ (outside the black hole), along the event horizon, and along future null infinity. In all three asymptotic regions we find that, after the decay of the quasi-normal modes, the perturbations are dominated by inverse power-law tails. The corresponding power indices agree with the integer values predicted by linearized theory. We also study the case of a charged black hole nonlinearly perturbed by a (neutral) self-gravitating scalar field, and find the same type of behavior---i.e., quasi-normal modes followed by inverse power-law tails, with the same indices as in the uncharged case.Comment: 14 pages, standard LaTeX, 18 Encapsulated PostScript figures. A new convergence test and a determination of QN ringing were added, in addition to correction of typos and update of reference