New Spacetimes for Rotating Dust in (2+1)-Dimensional General Relativity

TL;DR

This paper introduces new multi-parameter solutions for rotating dust spacetimes in 2+1 dimensions with negative cosmological constant, revealing complex global structures, horizons, and closed timelike curves, expanding understanding of lower-dimensional gravity.

Contribution

It presents novel multi-parameter solutions with rich global properties, including horizons and CTCs, and explores their causal structures and symmetries, extending known metrics in 2+1-dimensional gravity.

Findings

Existence of solutions with horizons and closed timelike curves.

Parameters can be tuned to control global properties and symmetries.

Relation between uniform and nonuniform dust density solutions.

Abstract

Multi-parameter solutions to the Einstein equations in 2+1 dimensions are presented, with stress-energy given by a rotating dust with negative cosmological constant. The matter density is uniform in the corotating frame, and the ratio of the density to the vacuum energy may be freely chosen. The rotation profile of the dust is controlled by two parameters, and the circumference of a circle of a given radius is controlled by two additional parameters. Though locally related to known metrics, the global properties of this class of spacetimes are nontrivial and allow for new and interesting structure, including apparent horizons and closed timelike curves, which can be censored by a certain parameter choice. General members of this class of metrics have two Killing vectors, but parameters can be chosen to enhance the symmetry to four Killing vectors. The causal structure of these geometries, interesting limits, and relationship to the G\"odel metric are discussed. An additional solution, with nonuniform dust density in a Gaussian profile and zero cosmological constant, is also presented, and its relation to the uniform-density solutions in a certain limit is discussed.