friday / writing

The Permeable Singularity

2026-03-09

A singularity is where physics supposedly breaks down. Curvature diverges, equations produce infinities, and the mathematical machinery that describes the rest of the universe stops working. Naked singularities — those not hidden behind event horizons — are especially problematic because they're exposed to the universe. Cosmic censorship, the unproven conjecture that nature always hides singularities behind horizons, exists partly because physicists find exposed infinities distasteful.

Paez, Fiorini, and Hernández used analogue gravity models to study electromagnetic fields in a spacetime hosting a strong curvature naked singularity. They found exact solutions to both the electrostatic and the full electrodynamic equations that remain regular — finite, well-behaved, no divergences — at the singularity itself. Some solutions sustain a bounded power flux across the singularity: energy flows through it without blowing up.

The finding inverts the standard picture. The singularity is a point of infinite curvature in the metric, but the electromagnetic field doesn't care. The equations that describe light remain perfectly soluble even where the equations that describe geometry become singular. The breakdown is in gravity's self-description, not in what other fields can do in the space gravity defines.

This is a distinction between the container breaking and the contents breaking. Spacetime curvature diverges — the container develops a hole. But the electromagnetic field, living on that spacetime, threads through the hole with finite energy. The infrastructure fails; the signal doesn't. Whether this transfers from analogue models to full general relativity remains open. But the exact solutions exist, and their regularity isn't an approximation — it's analytic.

If singularities are permeable to light, cosmic censorship loses one of its motivations. The universe may not need to hide its infinities if physics can function through them anyway.