# The Wafold: Curvature-Driven Termination and Dimensional Compression in Black Holes

## TL;DR

This paper proposes a new geometric model of black holes where spacetime ends at a curvature-triggered boundary called the wafold, instead of a singularity.

## Contribution

The novel concept is the wafold, a curvature-driven boundary where spatial dimensions compress into a surface, merging ideas from geometric compression and the holographic principle.

## Key findings

- A dimensional conversion law is derived to describe how spatial volume collapses into surface area at the wafold.
- The wafold is proposed as a terminal boundary where mass–energy and information are confined, eliminating the need for an interior singularity.
- The model aligns with the holographic principle by suggesting information is encoded on the boundary rather than in the bulk.

## Abstract

This work explores a geometric description of black holes in which spacetime terminates on a curvature-triggered hypersurface rather than extending to an interior singularity. We study the implications of a scenario in which, upon reaching a critical curvature threshold, the three-dimensional spatial geometry compresses into a thin, closed boundary identified here as the wafold. Beyond this, the manifold would no longer continue, and all mass–energy and information would be confined to the hypersurface itself. This framework combines two well-explored paths: (1) curvature-driven geometric compression, in which extreme curvature forces the bulk degrees of freedom to become supported on a thin hypersurface (without altering the underlying dimensionality of spacetime), and (2) the motivation underlying the holographic principle, namely that black-hole entropy scales with surface area rather than volume, suggesting that information is governed by a boundary geometry rather than a bulk volume. We elaborate a dimensional conversion law that would be required to describe the collapse of spatial volume into surface area as a conserved flux of geometric capacity across the wafold, and we analyze the resulting consequences of treating this hypersurface as the terminal boundary of the manifold.