Inside the BTZ black hole

Abstract

We consider a static circularly symmetric solution of three-dimensional Einstein equations with a negative cosmological constant (the BTZ black hole). The case of the zero cosmological constant corresponding to the interior region of a black hole is analyzed in detail. We prove that the maximally extended BTZ solution with the zero cosmological constant coincides with flat three-dimensional Minkowskian space-time without any singularities and horizons. The Euclidean version of this solution is shown to have a physical interpretation in the geometric theory of defects in solids describing combined wedge and screw dislocations.