Closed timelike curves and geodesics of Godel-type metrics

It is shown explicitly that when the characteristic vector field that defines a Godel-type metric is also a Killing vector, there always exist closed timelike or null curves in spacetimes described by such a metric. For these geometries, the geodesic curves are also shown to be characterized by a lower dimensional Lorentz force equation for a charged point particle in the relevant Riemannian background. Moreover, two explicit examples are given for which timelike and null geodesics can never be closed.Comment: REVTeX 4, 12 pages, no figures; the Introduction has been rewritten, some minor mistakes corrected, many references adde

Chain of refined perception in self-optimizing assembly of micro-optical systems

Today, the assembly of laser systems requires a large share of manual operations due to its complexity regarding the optimal alignment of optics. Although the feasibility of automated alignment of laser optics has been shown in research labs, the development effort for the automation of assembly does not meet economic requirements – especially for low-volume laser production. This paper presents a model-based and sensor-integrated assembly execution approach for flexible assembly cells consisting of a macro-positioner covering a large workspace and a compact micromanipulator with camera attached to the positioner. In order to make full use of available models from computer-aided design (CAD) and optical simulation, sensor systems at different levels of accuracy are used for matching perceived information with model data. This approach is named "chain of refined perception", and it allows for automated planning of complex assembly tasks along all major phases of assembly such as collision-free path planning, part feeding, and active and passive alignment. The focus of the paper is put on the in-process image-based metrology and information extraction used for identifying and calibrating local coordinate systems as well as the exploitation of that information for a part feeding process for micro-optics. Results will be presented regarding the processes of automated calibration of the robot camera as well as the local coordinate systems of part feeding area and robot base

Electrified Fuzzy Spheres and Funnels in Curved Backgrounds

We use the non-Abelian DBI action to study the dynamics of $N$ coincident $Dp$-branes in an arbitrary curved background, with the presence of a homogenous world-volume electric field. The solutions are natural extensions of those without electric fields, and imply that the spheres will collapse toward zero size. We then go on to consider the $D1-D3$ intersection in a curved background and find various dualities and automorphisms of the general equations of motion. It is possible to map the dynamical equation of motion to the static one via Wick rotation, however the additional spatial dependence of the metric prevents this mapping from being invertible. Instead we find that a double Wick rotation leaves the static equation invariant. This is very different from the behaviour in Minkowski space. We go on to construct the most general static fuzzy funnel solutions for an arbitrary metric either by solving the static equations of motion, or by finding configurations which minimise the energy. As a consistency check we construct the Abelian $D3$-brane world-volume theory in the same generic background and find solutions consistent with energy minimisation. In the $NS$5-brane background we find time dependent solutions to the equations of motion, representing a time dependent fuzzy funnel. These solutions match those obtained from the $D$-string picture to leading order suggesting that the action in the large $N$ limit does not need corrections. We conclude by generalising our solutions to higher dimensional fuzzy funnels.Comment: 38 pages, Latex; references adde

A pp-Wave With 26 Supercharges

A pp-wave solution to 11-dimensional supergravity is given with precisely 26 supercharges. Its uniqueness and the absence of 11-dimensional pp-waves which preserve (precisely) 28 or 30 supercharges is discussed. Compactification on a spacelike circle gives a IIA configuration with all 26 of the supercharges. For this compactification, D0 brane charge does not appear in the supersymmetry algebra. Indeed, the 26 supercharge IIA background does not admit any supersymmetric D-branes. In an appendix, a 28 supercharge IIB pp-wave is presented along with its supersymmetry algebra.Comment: 18 pages REVTeX 4 and AMSLaTeX. v3: Equations (III.17) and (III.18) corrected. Reference added. v4: more typos corrected and references adde

Black holes in Goedel-type universes with a cosmological constant

We discuss supersymmetric black holes embedded in a Goedel-type universe with cosmological constant in five dimensions. The spacetime is a fibration over a four-dimensional Kaehler base manifold, and generically has closed timelike curves. Asymptotically the space approaches a deformation of AdS_5, which suggests that the appearance of closed timelike curves should have an interpretation in some deformation of D=4, N=4 super-Yang-Mills theory. Finally, a Goedel-de Sitter universe is also presented and its causal structure is discussed.Comment: 25 pages, Latex, no figures, references updated, physical discussion of the solutions considerably expanded, holographic stress tensor and conserved charges of Goedel-AdS(5) solution compute

Non-Abelian Giant Gravitons

We argue that the giant graviton configurations known from the literature have a complementary, microscopical description in terms of multiple gravitational waves undergoing a dielectric (or magnetic moment) effect. We present a non-Abelian effective action for these gravitational waves with dielectric couplings and show that stable dielectric solutions exist. These solutions agree in the large $N$ limit with the giant graviton configurations in the literature.Comment: 8 pages. Contribution to the proceedings of the RTN workshop in Leuven, Belgium, September 200

Classical glueballs in non-Abelian Born-Infeld theory

It is shown that the Born-Infeld-type modification of the quadratic Yang-Mills action suggested by the superstring theory gives rise to classical particle-like solutions prohibited in the standard Yang-Mills theory. This becomes possible due to the scale invariance breaking by the Born-Infeld non-linearity. New classical glueballs are sphaleronic in nature and exhibit a striking similarity with the Bartnik-McKinnon solutions of the Yang-Mills theory coupled to gravity.Comment: Revtex, 4 pages, 2 eps figure

Homogeneous Plane-wave Spacetimes and their Stability

We consider the stability of spatially homogeneous plane-wave spacetimes. We carry out a full analysis for plane-wave spacetimes in (4+1) dimensions, and find there are two cases to consider; what we call non-exceptional and exceptional. In the non-exceptional case the plane waves are stable to (spatially homogeneous) vacuum perturbations as well as a restricted set of matter perturbations. In the exceptional case we always find an instability. Also we consider the Milne universe in arbitrary dimensions and find it is also stable provided the strong energy condition is satisfied. This implies that there exists an open set of stable plane-wave solutions in arbitrary dimensions.Comment: 15 pages, no figures; minor changes, new references, to appear in CQ

String theory and the Classical Stability of Plane Waves

The presence of fields with negative mass-squared typically leads to some form of instability in standard field theories. The observation that, at least in the light-cone gauge, strings propagating in plane wave spacetimes can have worldsheet scalars with such tachyon-like masses suggests that the supergravity background may itself be unstable. To address this issue, we perform a perturbative analysis around the type IIB vacuum plane wave, the solution which most obviously generates worldsheet scalars with negative mass-squared. We argue that this background is perturbatively stable.Comment: 23 pages, no figures; v2: very minor changes, references added, version accepted by PR

Supersymmetric Godel-type Universe in four Dimensions

We generalize the classification of all supersymmetric solutions of pure N=2, D=4 gauged supergravity to the case when external sources are included. It is shown that the source must be an electrically charged dust. We give a particular solution to the resulting equations, that describes a Goedel-type universe preserving one quarter of the supersymmetries.Comment: 6 pages, Latex. v2: references and footnote added. v3: introduction expanded, minor corrections, references added. Final versio