Gravitational Memory Charges of Supertranslation and Superrotation on Rindler Horizons

TL;DR

The paper develops a general framework for gravitational holographic charges on Rindler horizons in a (1+3)-dimensional linearized gravity setting, showing that matter crossing the horizon induces memory while the horizon charges remain well-defined and, at linear order, time-independent after absorption. The core result is an explicit surface-charge formula $Q[\xi]$ capturing supertranslation and superrotation charges in terms of horizon data, alongside a quantum memory operator $\hat{M}$ that encodes information about infalling matter but exhibits noncommutativity and contextuality with detectors. It demonstrates that gravitational waves do not shift these charges at leading order, while matter does, and proposes that the physical reality of holographic charges is conditioned on continuous near-horizon metric measurements to resolve potential no-cloning issues. The work thus connects horizon symmetries, memory effects, and information-theoretic concerns in a framework that may inform the black hole information problem and the interpretation of horizon hair.

Abstract

In a Rindler-type coordinate system spanned in a region outside of a black hole horizon, we have nonvanishing classical holographic charges as soft hairs on the horizon for stationary black holes. Taking a large black hole mass limit, the spacetimes with the charges are described by asymptotic Rindler metrics. We construct a general theory of gravitational holographic charges for a (1+3)-dimensional linearized gravity field in the Minkowski background with Rindler horizons. Although matter crossing a Rindler horizon causes horizon deformation and a time-dependent coordinate shift, that is, gravitational memory, the supertranslation and superrotation charges on the horizon can be defined during and after its passage through the horizon. It is generally proven that holographic states on the horizon cannot store any information about absorbed perturbative gravitational waves. However, matter crossing the horizon really excites holographic states. By using gravitational memory operators, which consist of the holographic charge operators, we suggest a resolution of the no-cloning paradox of quantum information between matter falling into the horizon and holographic charges on the horizon from the viewpoint of the contextuality of quantum measurement.

Figures (9)

• Figure 1: (Left) The near-horizon coordinate system of HPS is physically implemented by free-falling block-numbered clocks distributed in the space. In this coordinate system, classical holographic charges $Q[\xi]$ on the horizon vanish for stationary black holes. (Right) A coordinate system implemented by accelerating block-numbered clocks distributed in the space near the horizon. In this coordinate system, non-zero classical holographic charges $Q[\xi]$ appear on the horizon as soft black hole hair even for stationary black holes. The appearance of the charges in the accelerated coordinate system is reminiscent of that of a thermal bath in the Unruh effect.
• Figure 2: (Left) Collapsing matter information is imprinted in holographic charge states of asymptotic symmetries on the horizon. (Right) After throwing additional matter, the new holographic charge states have to carry whole information: original + additional.
• Figure 3: In the large mass limit of the black hole where each horizon coincides with one of the Rindler horizons, we potentially have duplicated quantum information.
• Figure 4: Gravitational memory defined with supertranslation and superrotation charges; each horizon plays the role of a holographic screen which stores matter information.
• Figure 5: A quantum wavepacket in an excited state $\ket{\Psi}$, created by applying a local unitary operator $\hat{U}$ comes across a future Rindler horizon.