Normal mode analysis for scalar fields in BTZ black hole background
Sayan K Chakrabarti, Pulak Ranjan Giri, Kumar S. Gupta
TL;DR
This paper investigates the boundary conditions for scalar fields in BTZ black hole backgrounds, revealing a family of self-adjoint extensions and implications for the space-time's quantum completeness.
Contribution
It introduces a method to determine the spectra of the Klein-Gordon operator considering boundary conditions in BTZ black holes.
Findings
Existence of a one-parameter family of self-adjoint extensions for certain parameters.
BTZ space-time can be quantum mechanically incomplete under specific conditions.
Proposed a physically motivated approach to spectral analysis.
Abstract
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.
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