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Based on an investigation into the near-horizon geometrical description ofblack hole spacetimes (the so-called "($r$,$t$) sector"), we find that thesurface area of the event horizon of a black hole is mirrored in the area of anewly-defined surface, which naturally emerges from studying the intrinsiccurvature of the ($r$,$t$) sector at the horizon. We define this new, abstractsurface for a range of different black holes and show that, in each case, thesurface encodes event horizon information, despite its derivation relyingpurely on the ($r$,$t$) sector of the metrical description. This is a verysurprising finding as this sector is orthogonal to the sector explicitlydescribing the horizon geometry. Our results provide new evidence supportingthe conjecture that black holes are, in some sense, fundamentallytwo-dimensional. As black hole entropy is known to be proportional to horizonarea, a novel two-dimensional interpretation of this entropy may also bepossible.

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