CAUCHY HORIZON INSTABILITY FOR REISSNER-NORDSTROM BLACK-HOLES IN DE SITTER SPACE

The radiative tail of gravitational and electromagnetic perturbations accumulates at the Cauchy horizon of a Reissner-Nordstrom black hole, producing an instability of that horizon. This instability is usually interpreted as an infinite proper-time compression effect: a free-falling observer crossing the Cauchy horizon sees an infinite number of waves within a finite proper time, hence measuring infinite energy densities. We show in this paper, using a simple model in which a Reissner-Nordstrom black hole immersed in de Sitter space is perturbed by a radial stream of infalling lightlike particles, that proper-time compression, though sufficient, is not a necessary condition for the instability of the Cauchy horizon. In our model, the Cauchy horizon is unstable whenever the surface gravity of the Cauchy horizon is greater than that of the cosmological horizon, in spite of the fact that there is no corresponding infinite proper-time compression.