Stationary strings and principal Killing triads in 2 + 1 gravity Original Research Article

A new tool for the investigation of (2 + 1)-dimensional gravity is proposed. It is shown that in a stationary (2 + 1)-dimensional space-time, the eigenvectors of the covariant derivative of the timelike Killing vector form a rigid structure, the principal Killing triad. Two of the triad vectors are null, and in many respects they play the role similar to the principal null directions in the algebraically special 4D space-times. It is demonstrated that the principal Killing triad can be efficiently used for classification and study of stationary 2 + 1 space-times.