Piecewise Flat Gravity in 3+1 dimensions

TL;DR

This paper explores a 3+1 dimensional gravity model inspired by 2+1 dimensions, where space is flat without matter and matter appears as conical defects, revealing emergent gravitational waves in the continuum limit.

Contribution

It introduces a flat-space gravity model with matter as conical defects and analyzes its dynamics, including collision behavior and emergent gravitational waves.

Findings

Collision dynamics are incomplete for high-energy defects.

No fully consistent dynamic completion for certain collisions.

Gravitational waves emerge in the continuum limit despite fundamental flatness.

Abstract

We study a model for gravity in 3+1 dimensions, inspired in general relativity in 2+1 dimensions. In contrast regular general relativity in 3+1 dimensions, the model postulates that space in absence of matter is flat. The requirement that the Einstein equation still holds for the complete spacetime, implies that matter may only appear as conical defects of co-dimension 2, which may be interpreted as straight cosmic strings moving at a constant velocity. The study of collisions of these defects reveals that the dynamics of the model is incomplete. Certain highly energetic collisions of almost parallel defects suggest that no dynamic completion may exist that is fully compatible with the principles on which the model was based. We also study the phase space of the model in the continuum limit. We find that even though does not contain gravitational waves at the fundamental level, they do appear as an emergent feature in the continuum limit.