Black Hole Event Horizon Oblateness Relative to a Dimensional Rupture

This paper calculates the event-horizon oblateness of a non-spinning black hole within the dimensional-rupture framework. A finite, planar, circular rupture with isotropic coupling produces a geometrically anisotropic effective force in the surrounding space despite being isotropic within its own plane. By deriving closed-form force expressions along equatorial and axial directions and imposing an equal-force condition at the horizon, the analysis obtains a direct relation between the rupture-to-horizon ratio and the resulting horizon oblateness. Significant oblateness emerges as the rupture-to-horizon ratio approaches unity, while spherical symmetry is rapidly recovered when the rupture is much smaller than the horizon. The resulting deformation is purely geometric and distinct from spin-induced horizon deformation, providing a calculable prediction of the rupture framework and a basis for extensions to rotating black holes and less symmetric rupture geometries.