Quantum memory for Rindler supertranslations

The Rindler horizon in Minkowski spacetime can be implanted with supertranslation hair by a matter shock wave without planar symmetry, and the hair is observable as a supertranslation memory on the Rindler family of uniformly linearly accelerated observers. We show that this classical memory is accompanied by a supertranslation quantum memory that modulates the entanglement between the opposing Rindler wedges in quantum field theory. A corresponding phenomenon across a black hole horizon may play a role in Hawking, Perry, and Strominger’s proposal for supertranslations to provide a solution to the black hole information paradox.

Figure 1

A null shell in the Rindler spacetime, with the transverasse dimensions suppressed. In the past of the shell the metric is given by (2.1), and the shell is at $V=V_0>0$. The four Rindler quadrants are labeled in the figure by I, II, III, and IV, and selected orbits of the boost Killing vector $\overline{\xi }$ (2.3) are shown in quadrant I. The coordinates in (2.5) cover both the future of the shell and the region $0<V<V_0$ of the past of the shell, and in these coordinates the shell is at $v=v_0$.

Figure 2

A pair of uniformly accelerated observers in the shock wave spacetime of Fig. 1. Luke (L) accelerates leftward in quadrant II. Rob (R) accelerates rightward in quadrant I, crossing the wave. After crossing the wave, Rob’s trajectory is no longer a pure hyperbola in the two dimensions shown in the diagram, but it involves a perturbative correction due to the wave [24]. Luke couples to field modes labeled $A$ and $C$. Rob couples before the wave-crossing to field modes labeled $B$ and $D$, and after the wave-crossing to field modes labelled $\overline{B}$ and $\overline{D}$.

Figure 3

The extended Schwarzschild spacetime with an infalling, supertranslation-implanting shock wave at $v=v_0$ [2]. Two Hawking pairs are shown, $A\leftrightarrow B$ (red) and $C\leftrightarrow D$ (blue).