Displacement memory effect near the horizon of black holes

Abstract: We study the displacement memory effect and its connection with the extended-BMS symmetries near the horizon of black holes. We show there is a permanent shift in the geodesic deviation vector relating two nearby timelike geodesics placed close to the horizon of black holes, upon the passage of gravitational waves. We also relate this memory effect with the asymptotic symmetries near the horizon of asymptotic black hole spacetimes. The shift of the relative position of the detectors is shown to be induced by a combination of BMS generators near the horizon. The displacement memory effect near the horizon possesses similarities to the same obtained in the far region.