976 research outputs found

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

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    We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities along a graph Γ\Gamma. We impose physically relevant conditions on the cone singularities, e.g. positivity of mass (angle less than 2π2\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 Γ\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

    Transversals to Line Segments in Three-Dimensional Space

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    We completely describe the structure of the connected components of transversals to a collection of n line segments in R3. We show that n \u3e 3 arbitrary line segments in R3 admit 0, 1, . . . , n or infinitely many line transversals. In the latter case, the transversals form up to n connected components
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