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Black hole memory effect

Laura Donnay, Gaston Giribet, Hernan A. Gonzalez, Andrea Puhm

TL;DR

This work establishes a concrete link between the memory effect produced by gravitational shocks at black hole horizons and the infinite-dimensional BMS symmetries at null infinity. By analyzing the near-horizon region of Schwarzschild and Reissner–Nordström black holes, the authors show that a BMS supertranslation at infinity corresponds to a combination of horizon supertranslation and horizon superrotation, with matching charges in both regions. Extending the analysis to Einstein–Maxwell theory reveals an enlarged current algebra acting on horizon data and clarifies how horizon charges encapsulate entropy changes and electromagnetic properties. The results generalize the memory effect to charged horizons and highlight the deep connection between asymptotic and near-horizon symmetries, while also raising questions about the physical interpretation of these horizon charges in a teleological, transitory setting.

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-Nordström black holes.

Black hole memory effect

TL;DR

This work establishes a concrete link between the memory effect produced by gravitational shocks at black hole horizons and the infinite-dimensional BMS symmetries at null infinity. By analyzing the near-horizon region of Schwarzschild and Reissner–Nordström black holes, the authors show that a BMS supertranslation at infinity corresponds to a combination of horizon supertranslation and horizon superrotation, with matching charges in both regions. Extending the analysis to Einstein–Maxwell theory reveals an enlarged current algebra acting on horizon data and clarifies how horizon charges encapsulate entropy changes and electromagnetic properties. The results generalize the memory effect to charged horizons and highlight the deep connection between asymptotic and near-horizon symmetries, while also raising questions about the physical interpretation of these horizon charges in a teleological, transitory setting.

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-Nordström black holes.

Paper Structure

This paper contains 8 sections, 77 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Gravitational shockwaves and BMS hair
  3. Soft hair on Schwarzschild horizons
  4. Horizon symmetries for Einstein-Maxwell
  5. Non-extremal horizons
  6. Extremal horizons
  7. Soft hair on Reissner-Nordström horizons
  8. Conclusions

Figures (1)

  • Figure 1: Penrose diagram of a Schwarzschild black hole. The gravitational shockwave at $v=v_0$ describes a domain wall that divides the exterior geometry in two regions, each of them with different values of the asymptotic charges.