Let us denote by [itex]X^i=(1,\vec 0)[/itex] the Killing vector and by [itex]u^i(s)[/itex] a tangent vector of a geodesic, where [itex]s[/itex] is some affine parameter.
What physical significance do the scalar quantity [itex]X_iu^i[/itex] and its conservation hold? If any...? I have seen this in may books and exam questions. I wonder what it means...