Limit curve theorems in Lorentzian geometry

The subject of limit curve theorems in Lorentzian geometry is reviewed. A general limit curve theorem is formulated which includes the case of converging curves with endpoints and the case in which the limit points assigned since the beginning are one, two or at most denumerable. Some applications are considered. It is proved that in chronological spacetimes, strong causality is either everywhere verified or everywhere violated on maximizing lightlike segments with open domain. As a consequence, if in a chronological spacetime two distinct lightlike lines intersect each other then strong causality holds at their points. Finally, it is proved that two distinct components of the chronology violating set have disjoint closures or there is a lightlike line passing through each point of the intersection of the corresponding boundaries.Comment: 25 pages, 1 figure. v2: Misprints fixed, matches published versio

Causally simple inextendible spacetimes are hole-free

It is shown that causally simple inextendible spacetimes are hole-free, thus confirming the expectation that causal simplicity removes holes from spacetime. This result is optimal in the sense that causal simplicity cannot be weakened to causal continuity. Physically, it means that if there is some partial Cauchy hypersurface which, for some reason, does not fully develop its influence, then there is some discontinuity in the causal relation.Comment: Revtex4, 9 pages. v2: minor correction

On Fermat's principle for causal curves in time oriented Finsler spacetimes

In this work, a version of Fermat's principle for causal curves with the same energy in time orientable Finsler spacetimes is proved. We calculate the secondvariation of the {\it time arrival functional} along a geodesic in terms of the index form associated with the Finsler spacetime Lagrangian. Then the character of the critical points of the time arrival functional is investigated and a Morse index theorem in the context of Finsler spacetime is presented.Comment: 20 pages, minor corrections, references adde

The Geometry of Warped Product Singularities

In this article the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.Comment: 14 page

Basal melt rates beneath Whillans Ice Stream, West Antarctica

This is the published version, also available here: http://dx.doi.org/10.3189/002214310793146241.Basal water lubricates and enables the fast flow of the West Antarctic ice streams which exist under low gravitational driving stress. Identification of sources and rates of basal meltwater production can provide insight into the dynamics of ice streams and the subglacial hydrology, which remain insufficiently described by glaciological theory. Combining measurements and analytic modeling, we identify two regions where basal meltwater is produced beneath Whillans Ice Stream, West Antarctica. Downstream of the onset of shear crevasses, strong basal melt (20–50 mm a−1) is concentrated beneath the relatively narrow shear margins. Farther upstream, melt rates are consistently 3–7 mm a−1 across the width of the ice stream. We show that the transition in melt-rate patterns is coincident with the onset of shear margin crevassing and streaming flow and related to the development of significant lateral shear resistance, which reorganizes the resistive stress regime and induces a concentration of basal resistance adjacent to the shear margin. Finally, we discuss how downstream freeze-on in the ice-stream center coupled with melt beneath the shear margin might result in a slowing but widening ice stream

The N=2 superconformal bootstrap

In this work we initiate the conformal bootstrap program for N=2N=2 super-conformal field theories in four dimensions. We promote an abstract operator-algebraic viewpoint in order to unify the description of Lagrangian and non-Lagrangian theories, and formulate various conjectures concerning the landscape of theories. We analyze in detail the four-point functions of flavor symmetry current multiplets and of N=2N=2 chiral operators. For both correlation functions we review the solution of the superconformal Ward identities and describe their superconformal block decompositions. This provides the foundation for an extensive numerical analysis discussed in the second half of the paper. We find a large number of constraints for operator dimensions, OPE coefficients, and central charges that must hold for any N=2N=2 superconformal field theory

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

Recirculating aquaculture systems: Questions to ask before you invest

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