标题： 从梯子分子出发的零测地线 显示英文标题

标题： Null Geodesics from Ladder Molecules

摘要： 我们提出了一种在近似于2维闵可夫斯基时空区域的因果集中的零测地线的离散类比，其精神类似于Kronheimer和Penrose对抽象因果空间的“网格”和“光束”的定义。 因果集的类比是“梯子分子”，其横档是由元素对组成的，这些元素对大致对应于Barton等人提出的视界双原子。 在二维情况下，梯子分子会捕获一条对应于加宽或模糊的视界的零测地线带。 反过来，元素对之间的梯子存在性提供了一种将时域关系推广到因果集的方法。 对近似于2维闵可夫斯基时空区域的因果集的模拟显示，梯子分子在因果集中相当密集，并提供了类似光锥的网格。 此外，类似于时空中时域相关事件之间零测地线的唯一性，在这样的因果集中，任何由广义时域关系连接的元素对之间也存在唯一的梯子分子。 显示英文摘要

摘要： We propose a discrete analogue of null geodesics in causal sets that are approximated by a region of 2d Minkowski spacetime, in the spirit of Kronheimer and Penrose's "grids" and "beams" for an abstract causal space. The causal set analogues are "ladder molecules", whose rungs are linked pairs of elements corresponding loosely to Barton et al's horizon bi-atoms. In 2d a ladder molecule traps a ribbon of null geodesics corresponding to a thickened or fuzzed out horizon. The existence of a ladder between linked pairs of elements in turn provides a generalisation of the horismotic relation to causal sets. Simulations of causal sets approximated by a region of 2d Minkowski spacetime show that ladder molecules are fairly dense in the causal set, and provide a light-cone like grid. Moreover, similar to the uniqueness of null geodesics between horismotically related events in the spacetime, in such causal sets there is a unique ladder molecule between any two linked pairs which are related by the generalised horismotic relation.