Mass inflation in a D-dimensional Reissner-Nordstroem black hole: A hierarchy of particle accelerators?

We study the geometry inside the event horizon of perturbed D dimensional Reissner-Nordstroem-(anti)de Sitter type black holes showing that, similarly to the four dimensional case, mass inflation also occurs for D>4. First, using the homogeneous approximation, we show that an increase of the number of spatial dimensions contributes to a steeper variation of the metric coefficients with the areal radius and that the phenomenon is insensitive to the cosmological constant in leading order. Then, using the code reported in [P. P. Avelino, A. J. S. Hamilton, and C. A. R. Herdeiro, Phys. Rev. D 79, 124045 (2009).] adapted to D dimensions, we perform fully nonlinear numerical simulations. We perturb the black hole with a compact pulse adapting the pulse amplitude such that the relative variation of the black hole mass is the same in all dimensions and determine how the black hole interior evolves under the perturbation. We qualitatively confirm that the phenomenon is similar to four dimensions as well as the behavior observed in the homogeneous approximation. We speculate about the formation of black holes inside black holes triggered by mass inflation, and about possible consequences of this scenario.