Quantum singularities in the BTZ spacetime

TL;DR

This paper investigates whether quantum test particles can resolve classical singularities in the negative mass BTZ spacetime, finding that certain particles 'heal' the singularity while others do not.

Contribution

It demonstrates that quantum particles obeying Klein-Gordon and Dirac equations can remove the classical singularity in the BTZ spacetime under specific conditions.

Findings

Massless scalar particles and fermions do not require additional boundary conditions near the singularity.

Massive scalar particles require extra boundary conditions to address the singularity.

The singularity is 'healed' for certain quantum particles, indicating quantum effects can resolve classical singularities.

Abstract

The spinless Ba\~nados-Teiltelboim-Zanelli (BTZ) spacetime is considered in the quantum theory context. Specially, we study the case of negative mass parameter using quantum test particles obeying the Klein-Gordon and Dirac equations. We study if this classical singular spacetime, with a naked singularity at the origin, remains singular when tested with quantum particles. The need of additional information near the origin is confirmed for massive scalar particles and all the possible boundary conditions necessary to turn the spatial portion of the wave operator self-adjoint are found. When tested by massless scalar particles or fermions, the singularity is ``healed'' and no extra boundary condition are needed. Near infinity, no boundary conditions are necessary.