BLACK-HOLES IN DE SITTER SPACE AND THE STABILITY CONJECTURE OF CAUCHYHORIZONS

The stability conjecture of Cauchy horizons of black holes suggested b y Helliwell and Konkowski is used to investigate the Reissner-Nordstro m-de Sitter black holes under perturbations of infalling null dust and of both outgoing and infalling null dust. The result given by this co njecture agrees with that from the exact back-reaction calculations: t he Cauchy horizon of the black hole is unstable when kappa(i) > kappa( c) and stable when kappa(i) < kappa(c), where kappa(i) and kappa(c) re present, respectively, the surface gravities of the Cauchy horizon and of the cosmological horizon. By using this conjecture we also study t he stability of the Cauchy horizon of the Kerr-de Sitter black holes, and predict that their result is similar to that of the Reissner-Nords trom-de Sitter black holes.