Abstract
We compute the memory effect produced at the black hole horizon by a transient gravitational shockwave. As shown by Hawking, Perry, and Strominger (HPS) such a gravitational wave produces a deformation of the black hole geometry which from future null infinity is seen as a Bondi-Metzner-Sachs (BMS) supertranslation. This results in a diffeomorphic but physically distinct geometry which differs from the original black hole by their charges at infinity. Here we give the complementary description of this physical process in the near-horizon region as seen by an observer hovering just outside the event horizon. From this perspective, in addition to a supertranslation the shockwave also induces a horizon superrotation. We compute the associated superrotation charge and show that its form agrees with the one obtained by HPS at infinity. In addition, there is a supertranslation contribution to the horizon charge, which measures the entropy change in the process. We then turn to electrically and magnetically charged black holes and generalize the near-horizon asymptotic symmetry analysis to Einstein-Maxwell theory. This reveals an additional infinite-dimensional current algebra that acts non-trivially on the horizon superrotations. Finally, we generalize the black hole memory effect to Reissner-Nordstr\"{o}m black holes.
Highlights
Over the last few years we have learned that gravitational and gauge field dynamics in asymptotically Minkowski spacetime entails a rich mathematical structure whose relevance for physics had been largely overlooked. This observation led to a revision of the notion of vacua in gravity and gauge theories in asymptotically flat spacetimes, which is of crucial importance for the scattering problem. This mathematical structure, expressed in the emergence of an infinite set of symmetries, unveils a surprising connection among three previously known but seemingly disconnected topics: a) the soft theorems for the S matrix of gravity and gauge theories in asymptotically flat spacetimes [1], b) the enhanced symmetry group that governs the dynamics in the asymptotic region [2,3,4], and c) the memory effect produced by transient gravitational waves [5,6]
Motivated by the problem of establishing a connection between the symmetries emerging in the near-horizon region of black holes and the symmetries in the far asymptotic region, in this paper we studied the memory effect produced at the horizon by an incoming gravitational shock wave
From the point of view of an observer in the asymptotic region, this process was studied in Ref. [25], where it was shown that the shock wave produces a disturbance in the black hole geometry that can be interpreted as a BMS supertranslation at null infinity
Summary
Over the last few years we have learned that gravitational and gauge field dynamics in asymptotically Minkowski spacetime entails a rich mathematical structure whose relevance for physics had been largely overlooked. A similar process has recently been studied by Hawking, Perry, and Strominger (HPS) [25], who showed that a transient shock wave produces a disturbance in the spacetime corresponding to a BMS supertranslation at null infinity. This provides a concrete example of a physical process that endows a black hole with BMS hair of the type suggested in Ref. This shows that, in addition to horizon supertranslations [22], horizon superrotations are crucial to describe the physics in the vicinity of the black hole This gives a bulk complementary description of the process studied in Ref.
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