space Nature Is Weird

All the complex 'layers' of a black hole—from its point of no return to its crushing center—are actually just different faces of a single mathematical object.

April 14, 2026

Original Paper

Geometrically Significant Surfaces of Black Holes from a Single Scalar

Cagdas Ulus Agca, Bayram Tekin

arXiv · 2604.10289

The Takeaway

Instead of treating the event horizon and the singularity as separate problems, this research derives them both from one single scalar function. It reveals a hidden unity in black hole geometry, showing that its most extreme features are just zeros and poles of the same master equation.

From the abstract

Black hole spacetimes contain several geometrically distinguished hypersurfaces, including event and Cauchy horizons, stationary-limit surfaces, curvature singularities, and asymptotic infinity. These structures are usually identified by different geometric or causal criteria. Here, we show that for the Kerr-Newman black hole, a single scalar function encodes all of them at once. The function arises by analytically continuing the membrane-paradigm pressure of the stretched horizon into the full