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

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.