ANALYTIC STUDY OF THE NULL SINGULARITY INSIDE SPHERICAL CHARGED BLACK-HOLES

We study analytically the features of the Cauchy horizon (CH) singular ity inside a spherically symmetric charged black hole, nonlinearly per turbed by a self-gravitating massless scalar field. We derive exact ex pressions for the divergence rate of the blue-shift factors, namely th e derivatives in the outgoing direction of the scalar field Psi and th e area coordinate r. Both derivatives are found to grow along the cont racting CH exactly like 1/r. Our results are valid everywhere along th e CH singularity, down to the point of full focusing. These exact anal ytic expressions are verified numerically.