Determine whether the primary torsion parameter is canonical hair

Determine whether the parameter \(\kappa_{3}\) defines an independent canonical hair within a fixed asymptotic phase space for the regular odd-parity axial-tensor black-hole solutions, taking into account the admissible Riemann–Cartan boundary conditions and associated conserved charges.

Background

The paper constructs regular black-hole solutions in the odd-parity axial-tensor sector with ADM mass $m_{\rm ADM}$ and an apparently independent torsion parameter $\kappa_{3}$. At the level of the local exact solutions, the authors state that these quantities can be varied independently by adjusting $\kappa_{2}$.

Whether this local independence persists as a genuine canonical hair in a fixed asymptotic phase space is left unresolved because it depends on the admissible Riemann–Cartan boundary conditions and the conserved charges associated with them. Establishing this requires an analysis beyond the local solution and its asymptotic expansion.