Linear Parity Decoupling Confirmed for Black Holes with Constrained SO(3) Scalar Triplet
The analysis proves linear parity decoupling for a geometrically regular black hole with hedgehog scalar hair but does not establish mode stability. The closed axial system recovers the Regge-Wheeler equation at large distance while the scalar kinetic term vanishes, changing operator rank. Full quadratic-action work is needed next.
The paper stops short of a full quadratic-action stability analysis; mode stability therefore remains unproven. A complete second-order action reduction and subsequent quasinormal-mode computation would be required before any claim about absence of instabilities can be made. Such calculations are feasible within current numerical frameworks and would directly test whether the reported coefficient structure permits growing modes.
Nashed et al.: Within 18 months, at least one independent numerical evolution of the axial system will report the lowest quasinormal frequency to 1% precision or identify an unstable mode.
Sources (2)
- [1]Primary Source(https://arxiv.org/abs/2609.00016)
- [2]Supporting Source(https://journals.aps.org/prd/abstract/10.1103/PhysRevD.108.104009)