Linearized 3D gravity with dust

TL;DR

This paper studies three-dimensional gravity coupled to dust, revealing that its physical degree of freedom behaves as an ultralocal field and can be characterized as either traceless or transverse in linearized flat spacetime.

Contribution

It demonstrates the ultralocal nature of the physical degree of freedom in 3D gravity with dust and provides linearized equations showing its dual traceless or transverse modes.

Findings

Physical degree of freedom is ultralocal, independent of spatial derivatives.

Linearized equations describe the mode as traceless or transverse.

Dynamics are encoded in the dust-time gauge, simplifying analysis.

Abstract

Three-dimensional gravity coupled to pressureless dust is a field theory with one local degree of freedom. In the canonical framework, the dust-time gauge encodes this physical degree of freedom as a metric function. We find that the dynamics of this field, up to spatial diffeomorphism flow, is independent of spatial derivatives and is therefore ultralocal. We also derive the linearized equations about flat spacetime, and show that the physical degree of freedom may be viewed as either a traceless or a transverse mode.