Abstract
The spinless Bañados-Teiltelboim-Zanelli spacetime is considered in the quantum theory context. Specifically, we study the case of a 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 for additional information near the origin is confirmed for massive scalar particles and all of 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 is needed. Near infinity, no boundary conditions are necessary.
- Received 28 February 2008
DOI:https://doi.org/10.1103/PhysRevD.77.124030
©2008 American Physical Society