Evolution of linear gravitational and electromagnetic perturbations insidea Kerr black hole - art. no. 024001

We analyze the evolution of linear gravitational (s = +/- 2) and electromag netic (s = +/- 1) perturbations inside a Kerr black hole, within the framew ork of the Newman-Penrose formalism. In particular, we derive explicit expr essions for the asymptotic behavior of the perturbations at the early porti on of the Cauchy horizon (CH). The calculation is carried out in the time d omain, using late-time expansion. The initial data are the presumed inverse -power tails at the event horizon. We find that the "outgoing" fields s<0 a re regular (though nonvanishing) at the CH. However, the ingoing" fields s> 0 diverge at the CH-like (r(-) r(-))(-s), where r is the radial Boyer-Lindq uist coordinate and r(-) is its value at the CH. This divergent term is mul tiplied by an inverse power of the ingoing Eddington coordinate upsilon. Fo r nonaxially symmetric modes (m = 0), the divergence of the s>0 fields is a lso modulated by an oscillatory term e(im Ohm_upsilon), where Ohm_ is a fix ed parameter and m is the magnetic number of the mode under consideration. This term exhibits an infinite number of oscillations on the approach to th e CH. We also find that the nonaxially symmetric modes diverge faster than the axially symmetric ones. Based on the result of a previous nonlinear per turbation expansion, which showed that the nonlinear perturbation terms are negligible at the CH compared to the linear ones, we argue that the linear gravitational perturbations calculated here correctly describe the strengt h and features of the curvature singularity at the CH (to the leading order in 1/upsilon and 1/u).