Normal mode analysis for scalar fields in BTZ black hole background
  We analyze the possibility of inequivalent boundary conditions for a scalar field propagating in the BTZ black hole space-time. We find that for certain ranges of the black hole parameters, the Klein-Gordon operator admits a one-parameter family of self-adjoint extensions. For this range, the BTZ space-time is not quantum mechanically complete. We suggest a physically motivated method for determining the spectra of the Klein-Gordon operator. 
Sayan K Chakrabarti, Pulak Ranjan Giri, Kumar S. Gupta