Displacement memory effect near the horizon of black holes

TL;DR

This paper investigates the displacement memory effect near black hole horizons, linking it to extended-BMS symmetries and showing a permanent geodesic shift caused by gravitational waves, similar to effects observed at infinity.

Contribution

It establishes a connection between horizon displacement memory and horizon BMS symmetries, revealing a permanent geodesic shift induced by gravitational waves near black holes.

Findings

Permanent shift in geodesic deviation vector near black hole horizons.

Displacement memory effect is related to horizon BMS symmetries.

Memory effect near the horizon resembles that at asymptotic infinity.

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.