Collisions of particles in locally AdS spacetimes I. Local description and global examples

We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities along a graph $\Gamma$. We impose physically relevant conditions on the cone singularities, e.g. positivity of mass (angle less than $2\pi$ on time-like singular segments). We construct examples of such manifolds, describe the cone singularities that can arise and the way they can interact (the local geometry near the vertices of $\Gamma$). We then adapt to this setting some notions like global hyperbolicity which are natural for Lorentz manifolds, and construct some examples of globally hyperbolic AdS manifolds with interacting particles.Comment: This is a rewritten version of the first part of arxiv:0905.1823. That preprint was too long and contained two types of results, so we sliced it in two. This is the first part. Some sections have been completely rewritten so as to be more readable, at the cost of slightly less general statements. Others parts have been notably improved to increase readabilit

Cosmological time versus CMC time I: Flat spacetimes

This paper gives a new proof that maximal, globally hyperbolic, flat spacetimes of dimension $n\geq 3$ with compact Cauchy hypersurfaces are globally foliated by Cauchy hypersurfaces of constant mean curvature, and that such spacetimes admit a globally defined constant mean curvature time function precisely when they are causally incomplete. The proof, which is based on using the level sets of the cosmological time function as barriers, is conceptually simple and will provide the basis for future work on constant mean curvature time functions in general constant curvature spacetimes, as well for an analysis of the asymptotics of constant mean foliations

Atypical haemolytic-uraemic syndrome caused by factor H mutation: case report and new management strategies in children

Atypical haemolytic uraemic syndrome is causedby alternative complement pathway dysregulation. It has recently been recognised that most cases are due to genetic factors and a growing list of mutations has been described. Atypical haemolytic uraemic syndrome is associated with a dismal prognosis, a relapsing course, high acute mortality and frequent progression to end-stage renal disease. We describe a five-year-old boy admitted with a first recurrence of atypical haemolytic uraemic syndrome. The primary onset of the disease was at 15 months of age, following which there was complete recovery of haematological and renal parameters. His family history was significant in that his mother had died at the age of only 23 years of a stroke with associated thrombotic microangiopathy, suggesting a familial form of the disease. Sequencing of the gene encoding complement factor H revealed a heterozygous SCR20 mutation (3644G>T, Arg1215Leu), confirming the diagnosis. The patient was successfully treated with fresh frozen plasma infusions that induced disease remission. We also review currently evolving concepts about atypical haemolytic uraemic syndrome caused by factor H mutation, its diagnosis, the role of genetic testing and management strategies in children

Geometry and observables in (2+1)-gravity

We review the geometrical properties of vacuum spacetimes in (2+1)-gravity with vanishing cosmological constant. We explain how these spacetimes are characterised as quotients of their universal cover by holonomies. We explain how this description can be used to clarify the geometrical interpretation of the fundamental physical variables of the theory, holonomies and Wilson loops. In particular, we discuss the role of Wilson loop observables as the generators of the two fundamental transformations that change the geometry of (2+1)-spacetimes, grafting and earthquake. We explain how these variables can be determined from realistic measurements by an observer in the spacetime.Comment: Talk given at 2nd School and Workshop on Quantum Gravity and Quantum Geometry (Corfu, September 13-20 2009); 10 pages, 13 eps figure

Particle Physics Explanations for Ultra High Energy Cosmic Ray Events

The origin of cosmic ray events with E \gsim 10^{11} GeV remains mysterious. In this talk I briefly summarize several proposed particle physics explanations: a breakdown of Lorentz invariance, the ``$Z-$burst'' scenario, new hadrons with masses of several GeV as primaries, and magnetic monopoles with mass below $10^{10}$ GeV as primaries. I then describe in a little more detail the idea that these events are due to the decays of very massive, long--lived exotic particles.Comment: Invited plenary talk at PASCOS03, Mumbai, India, January 2003; 13 pages, 1 figur

On The Injection Spectrum of Ultrahigh Energy Cosmic Rays in the Top-Down Scenario

We analyze the uncertainties involved in obtaining the injection spectra of UHECR particles in the top-down scenario of their origin. We show that the DGLAP $Q^2$ evolution of fragmentation functions (FF) to $Q=M_X$ (mass of the X particle) from their initial values at low $Q$ is subject to considerable uncertainties. We therefore argue that, for x\lsim 0.1 (the $x$ region of interest for most large $M_X$ values of interest, $x\equiv 2E/M_X$ being the scaled energy variable), the FF obtained from DGLAP evolution is no more reliable than that provided, for example, by a simple Gaussian form (in the variable $\ln(1/x)$) obtained under the Modified Leading Log Approximation (MLLA). Additionally, we find that for x\gsim0.1, the evolution in $Q^2$ of the singlet FF, which determines the injection spectrum, is ``minimal'' -- the singlet FF changes by barely a factor of 2 after evolving it over $\sim$ 14 orders of magnitude in $Q\sim M_X$. We, therefore, argue that as long as the measurement of the UHECR spectrum above \sim10^{20}\ev is going to remain uncertain by a factor of 2 or larger, it is good enough for most practical purposes to directly use any one of the available initial parametrisations of the FFs in the $x$ region x\gsim0.1 based on low energy data even without evolving them to the requisite $Q^2$ value.Comment: Minor changes, added a reference, version to appear in Phys. Rev.

Polygon model from first order gravity

The gauge fixed polygon model of 2+1 gravity with zero cosmological constant and arbitrary number of spinless point particles is reconstructed from the first order formalism of the theory in terms of the triad and the spin connection. The induced symplectic structure is calculated and shown to agree with the canonical one in terms of the variables.Comment: 20 pages, presentation improved, typos correcte

Notes on a paper of Mess

These notes are a companion to the article "Lorentz spacetimes of constant curvature" by Geoffrey Mess, which was first written in 1990 but never published. Mess' paper will appear together with these notes in a forthcoming issue of Geometriae Dedicata.Comment: 26 page