Non-spherical horizon topology in 4D beyond GR

Investigate whether black rings or other black objects with non-spherical horizon topology can exist in four spacetime dimensions within theories beyond General Relativity, thereby extending the higher-dimensional abundance of horizon topologies to 4D.

Background

In higher dimensions, black objects with non-spherical horizons (e.g., black rings, Saturns) are plentiful due to the flexibility of long horizons. In 4D GR, topological censorship forbids such objects, but beyond-GR theories may allow them.

This question probes whether modifying the gravitational sector could accommodate richer horizon topologies in 4D, paralleling the D>4 landscape.