Abstract

In this paper, we consider a litle-studied observable in classical pure AdS, gravity: the twist alonga geodesic.The motivation is that the twist only supports on the geodesic and may be a candidateelement in the center. We study the properties of the twist and get the following results. First, weget the system's evolution generated by the twist, which exhibits a relative shift along the geodesicSecond, we show that the twist commutes with the length of the same geodesic, which supports theproposal that the twist is a candidate element in the center.