Piecewise Flat Gravitational Waves

TL;DR

This paper analyzes a piecewise flat gravity model, deriving conditions for energy-momentum and showing that lightlike modes produce linear gravitational waves, despite their absence at the microscopic level.

Contribution

It provides a continuum limit analysis of 't Hooft's piecewise flat gravity model, revealing how gravitational waves emerge from microscopic defect configurations.

Findings

Energy--momentum tensor satisfies specific restrictions.

Metric perturbations include lightlike modes that mimic gravitational waves.

Gravitational waves emerge despite no microscopic waves present.

Abstract

We examine the continuum limit of the piecewise flat locally finite gravity model introduced by 't Hooft. In the linear weak field limit we find the energy--momentum tensor and metric perturbation of an arbitrary configuration of defects. The energy--momentum turns out to be restricted to satisfy certain conditions. The metric perturbation is mostly fixed by the energy--momentum except for its lightlike modes which reproduce linear gravitational waves, despite no such waves being present at the microscopic level.