Named for a
physicist by the name of
Killing, not for the type of action such a
vector might take, a Killing
vector is an important
concept in
General Relativity. It is a
tangent vector to a
trajectory along which the
metric tensor is
invariant. Taking the
inner product of a Killing
vector and a
vector tangent to a
geodesic produces a
constant of motion.
The existence of a timelike Killing vector implies that the spacetime is stationary.