Physical event horizons of noncorotating vacuum profiles

Determine the location and establish the global black-hole interpretation of the physical event horizon for stationary axisymmetric Kalb–Ramond vacuum profiles whose angular parameter \omega differs from the Kerr horizon angular velocity \Omega_H, including verification of a common smooth field extension, exterior causal structure, and global escape behavior.

Background

The paper constructs a family of exact vacuum geometries using alternative closed Kalb–Ramond two-forms parameterized by an angular parameter \omega. For \omega\neq\Omega_H, the auxiliary Kerr surface r=r_+ is not generally a physical null hypersurface when A\neq C. The authors derive a candidate equation for a possible stationary axisymmetric horizon r=\rho_\omega(\theta), but do not solve it or establish its global interpretation.

The analysis distinguishes profiles that are regular on the future or past extension and notes that the corotating profile is the one that preserves the regular physical Killing horizon at r=r_+. Other profiles remain exact exterior vacuum candidates, but their event-horizon location and the global conditions required for a black-hole interpretation are unresolved.