Caustics of world hyper-sheets in the Minkowski space-time

TL;DR

This paper develops a mathematical framework to analyze caustics of world hyper-sheets in Minkowski space-time, providing insights into their singularities and geometric properties, serving as a simplified model for more complex gravitational scenarios.

Contribution

It introduces a novel mathematical approach to describe caustics of world hyper-sheets, linking geometric singularities to holographic domain concepts in space-time.

Findings

Characterization of caustic singularities in Minkowski space-time

Connection between caustic geometry and holographic domains

A simplified model for gravitational caustics

Abstract

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.