A Killing vector field, or simply a Killing vector, after Wilhelm Killing origiantes from the argument that a metric may be invariant when every point in spacetime is systematically shifted by some in...A Killing vector field, or simply a Killing vector, after Wilhelm Killing origiantes from the argument that a metric may be invariant when every point in spacetime is systematically shifted by some infinitesimal amount. When all the points in a space are displaced as specified by the Killing vector, they flow without expansion or compression. Although the term “Killing vector” is singular, it refers to the entire field of vectors, each of which differs in general from the others.
