Cauchy-horizon singularity inside perturbed Kerr black holes

摘要

The Cauchy horizon inside a perturbed Kerr black hole develops an instabilitythat transforms it into a curvature singularity. We solve for the linearizedWeyl scalars $\psi_0$ and $\psi_4$ and for the curvature scalar$R_{\alpha\beta\gamma\delta}R^{\alpha\beta\gamma\delta}$ along outgoing nullrays approaching the Cauchy horizon in the interior of perturbed Kerr blackholes using the Teukolsky equation, and compare our results with those found inperturbation analysis. Our results corroborate the previous perturbationanalysis result that at its early parts the Cauchy horizon evolves into adeformationally-weak, null, scalar-curvature singularity. We find excellentagreement for $\psi_0(u={\rm const},v)$, where $u,v$ are advanced and retardedtimes, respectively. We do find, however, that the exponential growth rate of$R_{\alpha\beta\gamma\delta}R^{\alpha\beta\gamma\delta}(u={\rm const},v)$approaching the singularity is dramatically slower than that found inperturbation analysis, and that the angular frequency is in excellentagreement.