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In this paper, we consider a little-studied observable in classical pure AdS3gravity: the twist along a geodesic. The motivation is that the twist onlysupports on the geodesic so may be a candidate element in the center of thealgebra in either entanglement wedge associated to the geodesic. We study theproperties of the twist and get the following results. First, we get thesystem's evolution generated by the twist, which exhibits a relative shiftalong the geodesic. Second, we show that the twist commutes with the length ofthe same geodesic, which supports the proposal that the twist is a candidateelement in the center.

An Observable in Classical Pure AdS3 Gravity: the Twist along a Geodesic