Bound on Superradiant Amplification

Determine whether superradiant amplification factors in black hole and related spacetimes are universally bounded above by 100%, by proving the bound or providing explicit counterexamples across relevant coupling regimes and geometries.

Background

Using a WKB analysis around the turning point of the effective potential for wave scattering in charged/rotating spacetimes, the authors show that in the large-coupling regime the amplification factor saturates at 100%. This analytical prediction matches available numerical evidence across different geometries.

However, the generality of this upper bound has not been rigorously established. The authors frame this as a conjecture and point out that their result offers strong support but does not constitute a proof, leaving the broader question open.

References

This is one of our main results. The amplification factor saturates, for very large couplings q, at precisely 100\%. This prediction is consistent with all numerical results we are aware of, and includes other, more generic geometries than D-dimensional Reissner-Nordstr{\o}m. This result by itself does not guarantee that the amplification factors are bounded by 100\%, but do lend strong support to this conjecture.

— The Physics of Black Holes and Their Environments: Consequences for Gravitational Wave Science (2511.14841 - Cardoso et al., 18 Nov 2025) in Subsection “Large coupling limit and a WKB analysis” (Part II: Superradiance)