Towards exterior/interior correspondence of black-holes

Abstract

We describe a simple approach for a possible connection between the exterior and interior of black-holes. According to our result, the Schwarzschild radius determines a [Formula: see text]-dimensional sphere that separates two worlds: the exterior, where ordinary matter moves with velocities less than the light velocity, and the interior, where tachyons move with velocities greater than the light velocity. Moreover, we find a geometric map in the complex plane that connects ordinary matter with faster than light particles. Motivated by these results, we also find that the exterior and the interior structures of black-holes can be unified in a world of [Formula: see text]-dimensions. Finally, we comment about the possibility that superluminal particles in the interior of a black-hole may provide an alternative solution of the rotation curves of spiral galaxies.