Collisions in piecewise flat gravity in 3+1 dimensions

TL;DR

This paper explores collision resolution of string defects in a (3+1)-dimensional piecewise flat gravity model, introducing a new geometric approach and analyzing limitations imposed by causality constraints.

Contribution

It presents a novel geometric framework for string collision resolution in 3+1 dimensions and extends the analysis to more general collision scenarios.

Findings

Resolved a broader class of string collisions using geometric methods

Identified bounds on angles beyond which collision resolutions violate causality

Provided insights into the limitations of the model for certain defect configurations

Abstract

We consider the (3+1)-dimensional locally finite gravity model proposed by 't Hooft. In particular we revisit the problem of resolving collisions of string defects. We provide a new geometric description of the configurations of strings using piecewise flat manifolds, and use it to resolve a more general class of collisions. We argue that beyond certain bounds for the deficiency/surplus angles no resolutions may be found that satisfy the imposed causality conditions.