Hidden Depths in a Black Hole: Surface Area Information Encoded in the ($r$,$t$) Sector

TL;DR

This paper reveals that the surface area of a black hole's event horizon is encoded in a newly defined surface within the ($r$,$t$) sector, suggesting a fundamental two-dimensional nature of black holes and potential new insights into black hole entropy.

Contribution

The study introduces a new surface derived from the ($r$,$t$) sector that encodes horizon information across various black holes, highlighting a surprising link between this sector and horizon geometry.

Findings

Surface area mirrored in the new ($r$,$t$) sector surface

The new surface encodes event horizon information for different black holes

Supports the idea of black holes being fundamentally two-dimensional

Abstract

Based on an investigation into the near-horizon geometrical description of black hole spacetimes (the so-called "($r$,$t$) sector"), we find that the surface area of the event horizon of a black hole is mirrored in the area of a newly-defined surface, which naturally emerges from studying the intrinsic curvature of the ($r$,$t$) sector at the horizon. We define this new, abstract surface for a range of different black holes and show that, in each case, the surface encodes event horizon information, despite its derivation relying purely on the ($r$,$t$) sector of the metrical description. This is a very surprising finding as this sector is orthogonal to the sector explicitly describing the horizon geometry. Our results provide new evidence supporting the conjecture that black holes are, in some sense, fundamentally two-dimensional. As black hole entropy is known to be proportional to horizon area, a novel two-dimensional interpretation of this entropy may also be possible.