Directly observing entropy accumulate on the horizon and holography

TL;DR

This paper demonstrates that matter and entropy in gravitational collapse can be observed accumulating directly on the horizon surface in a specific foliation, supporting holographic principles and the horizon's role in information storage.

Contribution

It introduces a special foliation where entropy accumulates on the horizon, linking volume-based and horizon-based descriptions of black hole information.

Findings

Entropy accumulates on the horizon in the special foliation.

Matter and entropy distribution depends on the foliation choice.

Holography maps volume-residing information to horizon surface.

Abstract

Recent numerical simulations of gravitational collapse show that there exists a special foliation of the spacetime where matter and entropy accumulate directly on the inside of the horizon surface. In this foliation, the time coincides with the proper time of the asymptotic static observer (ASO) and for spherical symmetry, this corresponds to isotropic coordinates. In this gauge, the three-volume in the interior shrinks to zero and only the horizon area remains at the end of collapse. In a different foliation, matter and entropy accumulate in the volume. The entropy is however independent of the foliation. Black hole holography is therefore a mapping from an arbitrary foliation, where information resides in the volume, to the special ASO frame, where it resides directly on the horizon surface.