2015/03/31 by Shyuichi Izumiya, Izumiya, Shyuichi · 1 citation
Mathematics · #58K05 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:58K05
paper · pdf · doi:10.48550/arxiv.1503.08888
19 pages
arxiv created 2015/03/31 · arxiv updated 2015/04/01
In the Minkowski space-time, a world hyper-sheet is a timelike hypersurface consisting of a one-parameter family of spacelike submanifolds. Recently, Bousso and Randall introduced the notion of caustics of world hyper-sheets in order to define the notion of holographic domains in space-time. Here, we give a mathematical framework for describing the caustics of world hyper-sheets in the Minkowski space-time. As a consequence, we investigate the singularities of the caustics of world hyper-sheets and whose geometrical meanings. Although the Minkowski space-time has zero gravity, this framework gives a simple toy model for general cases.