LATE-TIME SINGULARITY INSIDE NONSPHERICAL BLACK-HOLES - ART. NO. 084034

It was long believed that the singularity inside a realistic, rotating black hole must be spacelike. However, studies of the internal geomet ry of black holes indicate a more complicated structure is typical. Wh ile it seems likely that an observer falling into a black hole with th e collapsing star encounters a crushing spacelike singularity, an obse rver falling in at late times generally reaches a null singularity whi ch is vastly different in character to the standard Belinsky, Khalatni kov, and Lifschitz (BKL) spacelike singularity [V. A. Belinsky, I. hi. Khalatnikov, and E. M. Lifshitz, Sov. Phys. JETP 32, 169 (1970)]. In the spirit of the classic work of BKL we present an asymptotic analysi s of the null singularity inside a realistic black hole. Motivated by current understanding of spherical models, we argue that the Einstein equations reduce to a simple form in the neighborhood of the null sing ularity. The main results arising from this approach are demonstrated using an almost plane symmetric model. The analysis shows that the nul l singularity results from the blueshift of the late-time gravitationa l wave tail; the amplitude of these gravitational waves is taken to de cay as an inverse power of advanced time as suggested by perturbation theory. The divergence of the Weyl curvature at the null singularity i s dominated by the propagating modes of the gravitational field, that is, C<INF>alpha beta gamma delta</INF>C<SUP>alpha beta gamma delta</SU P> similar to<SUP></SUP> Psi<INF>0</INF>Psi<INF>4</INF> similar to ups ilon<SUP>-(2l + 3</SUP>)e<SUP>2 kappa upsilon</SUP>, as upsilon --> in finity at the Cauchy horizon. Here, Psi<INF>0</INF> and Psi<INF>4</INF > are the Newman-Penrose Weyl scalars, and l greater than or equal to 2 is the multipole order of the perturbations crossing the event horiz on. The null singularity is weak in the sense that tidal distortion re mains bounded along timelike geodesics crossing the Cauchy horizon. Th ese results are in agreement with previous analyses of black hole inte riors. We briefly discuss some outstanding problems which must be reso lved before the picture of the generic black hole interior is complete . [S0556-2821(98)04118-6].