(2 + 1) noncommutative gravity and conical spacetimes

TL;DR

This paper solves (2+1) noncommutative gravity with point sources, showing continuity with classical Einstein gravity at large distances and small noncommutative parameter, while revealing limitations on mass and ambiguities in deficit angle measurement.

Contribution

It provides a solution to (2+1) noncommutative gravity coupled to point sources and analyzes the gauge invariance and classical limit behavior.

Findings

Continuity with Einstein gravity at large distances and small $ heta$

Limitations on the mass of sources in noncommutative gravity

Ambiguity in measuring the deficit angle due to gauge dependence

Abstract

We solve (2+1) noncommutative gravity coupled to point-like sources. We find continuity with Einstein gravity since we recover the classical gravitational field in the $\theta \to 0$ limit or at large distance from the source. It appears a limitation on the mass which is twice than expected. Since the distance is not gauge invariant, the measure of the deficit angle near the source is intrinsically ambiguous, with the gauge group playing the role of statistical ensemble. Einstein determinism can be recovered only at large distance from the source, compared with the scale of the noncommutative parameter $\sqrt{\theta}$.