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.

References

Open questions: Would it be possible to obtain black rings or other black objects with non-spherical horizon topology in four dimensions in some theory beyond GR?

— Black Holes Inside and Out 2024: visions for the future of black hole physics  (2410.14414 - Afshordi et al., 2024) in Roberto Emparan, Section "Black holes in higher dimensions"

It remains to determine whether these admit regular non-compact horizon sections, including planar or hyperbolic cases, or other global identifications.

— Generalized Black holes with Fully Non-aligned Electromagnetic Fields  (2609.10332 - Furugori et al., 9 Sep 2026) in Section 10, Summary and discussion, paragraph “Global structure and horizon topology”