Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-02-07
Nucl.Phys. B468 (1996) 336-354
Physics
High Energy Physics
High Energy Physics - Theory
28 pages, Latex. More references included
Scientific paper
10.1016/0550-3213(96)00140-X
A new tool for the investigation of 2+1 dimensional gravity is proposed. It is shown that in a stationary 2+1 dimensional spacetime, the eigenvectors of the covariant derivative of the timelike Killing vector form a rigid structure, the {\it 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 4-D spacetimes. It is demonstrated that the principal Killing triad can be efficiently used for classification and study of stationary 2+1 spacetimes. One of the most interesting applications is a study of minimal surfaces in a stationary spacetime. A {\it principal Killing surface} is defined as a surface formed by Killing trajectories passing through a null ray, which is tangent to one of the null vectors of the principal Killing triad. We prove that a principal Killing surface is minimal if and only if the corresponding null vector is geodesic. Furthermore, we prove that if the 2+1 dimensional spacetime contains a static limit, then the only regular stationary timelike minimal 2-surfaces that cross the static limit, are the minimal principal Killing surfaces. A timelike minimal surface is a solution to the Nambu-Goto equations of motion and hence it describes a cosmic string configuration. A stationary string interacting with a 2+1 dimensional rotating black hole is discussed in detail.
Frolov Valera
Hendy Shaun
Larsen Arne. L.
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