Extremal Kerr at the threshold in axisymmetric Einstein–Klein–Gordon

Determine whether an extremal Kerr black hole lies at the threshold of collapse in the axisymmetric 3+1 Einstein–Klein–Gordon system with a massless complex scalar field constrained by the single-mode ansatz ψ(ρ,φ,z,t)=e^{imφ}ψ_m(ρ,z,t), potentially requiring different families of initial data or the inclusion of a non-zero scalar mass term.

Background

The paper studies near-threshold collapse of a massless complex scalar field in axisymmetry under the Choptuik et al. single-mode ansatz, extending prior m=1 results to m=2. Motivated by recent rigorous results on extremal critical collapse in charged systems and conjectures about extremal Kerr formation at threshold, the authors examine whether extremality manifests in their axisymmetric Einstein–Klein–Gordon simulations.

Their data show that angular momentum becomes negligible near threshold and do not exhibit a trend toward extremality within the initial-data families considered. Nonetheless, they explicitly state that the possibility of an extremal Kerr critical solution in this model remains open, suggesting it may require substantially different families of initial data or the inclusion of a non-zero scalar mass term.