Characterization of three-dimensional Lorentzian metrics that admit four Killing vectors

TL;DR

This paper classifies three-dimensional Lorentzian metrics with four Killing vectors, providing conditions based on algebraic and differential properties of curvature tensors to identify such metrics.

Contribution

It offers a comprehensive classification and characterization criteria for 3D Lorentzian metrics admitting four Killing vectors, including algebraic and curvature conditions.

Findings

Classification of metrics with four Killing vectors

Conditions involving traceless Ricci tensor and curvature derivatives

Summary of algebraic and differential criteria

Abstract

We consider three-dimensional Lorentzian metrics that locally admit four independent Killing vectors. Their classification is summarized, and conditions for characterizing them are found. These consist of algebraic classification of the traceless Ricci tensor, and other conditions satisfied by the curvature and its derivative.