局部AdS时空中粒子的碰撞
Collisions of particles in locally AdS spacetimes
摘要：
我们研究了包含“粒子”的三维全局双曲AdS流形，即，图$Γ$上的锥奇点。我们对锥奇点施加物理上的相关条件，例如质量的正性（角度小于$2π$的类时奇异段）。我们构建这样的流形的例子，描述的锥奇点，可以出现和他们可以相互作用的方式（$Γ$的顶点附近的局部几何）。局部几何附近的“相互作用点”（一个顶点的奇异轨迹）有一个简单的几何描述多面体的扩展双曲3空间的de Sitter空间。然后，我们专注于只包含（相互作用）大质量粒子的空间。对于每一个这样的空间，我们关联一个图和一个有限族的双曲曲面对锥奇点。我们表明，这些数据足以在本地恢复空间（即，在固定度量的邻域中）。这是Mess关于非奇异整体双曲AdS流形的一个结果的部分推广。
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 $Γ$). The local geometry near an "interaction point" (a vertex of the singular locus) has a simple geometric description in terms of polyhedra in the extension of hyperbolic 3-space by the de Sitter space. We then concentrate on spaces containing only (interacting) massive particles. To each such space we associate a graph and a finite family of pairs of hyperbolic surfaces with cone singularities. We show that this data is sufficient to recover the space locally (i.e., in the neighborhood of a fixed metric). This is a partial extension of a result of Mess for non-singular globally hyperbolic AdS manifolds.
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