Inside the BTZ black hole

TL;DR

This paper investigates the interior of the BTZ black hole, showing that with zero cosmological constant, the solution is flat Minkowski space without singularities, and relates it to defect theory in solids.

Contribution

It provides a detailed analysis of the zero cosmological constant case of the BTZ black hole and links it to geometric defect theory in solids.

Findings

Maximally extended BTZ solution with zero cosmological constant is flat Minkowski space.

The Euclidean version relates to geometric defect theory in solids.

No singularities or horizons in the zero cosmological constant case.

Abstract

We consider static circularly symmetric solution of three-dimensional Einstein's equations with negative cosmological constant (the BTZ black hole). The case of 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 zero cosmological constant coincides with flat three-dimensional Minkowskian space-time without any singularity and horizons. The Euclidean version of this solution is shown to have physical interpretation in the geometric theory of defects in solids describing combined wedge and screw dislocations.