Stability of the extended Kerr–Bertotti–Robinson geometry

Determine whether the extended Kerr–Bertotti–Robinson spacetime is stable under perturbations, beyond the information provided by the quasinormal-mode analysis of a test massless scalar field.

Background

The paper constructs a smooth extension of the Kerr–Bertotti–Robinson spacetime across the surface r=∞, joining successive regions through wormhole-like bridges and exposing a neighboring ring singularity without an intervening horizon. Because this global structure challenges the usual black-hole interpretation and the weak cosmic censorship conjecture, the authors investigate its perturbative behavior using quasinormal modes of a test massless scalar field on a two-universe scattering segment.

The analysis establishes exponentially growing axisymmetric modes and finds additional unstable nonaxisymmetric branches, but the scattering region contains closed timelike curves and is not globally hyperbolic. Consequently, the computed growing modes do not by themselves settle whether the full extended geometry possesses a conventional dynamical instability under generic perturbations or Cauchy evolution.