arXiv 1010.36022010-10-18math.DGmath-phmath.GTmath.MP

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

Thierry Barbot, Francesco Bonsante, Jean-Marc Schlenker

备注：: 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 readability
发表信息：: Communications in Mathematical Physics 308(2011):1, 147-200
DOI：: 10.1007/s00220-011-1318-6

英文摘要：

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

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