Normal Modes and No Zero Mode Theorem of Scalar Fields in BTZ Black Hole   Spacetime
  Eigenfunctions for normal modes of scalar fields in BTZ black hole spacetime are studied. Orthonormal relations among them are derived. Quantization for scalar fields is done and particle number, energy and angular momentum are expressed by the creation and annihilation operators. Allowed physical normal mode region is studied on the basis of the no zero mode theorem. Its implication to the statistical mechanics is also studied. 
M. Kenmoku, M. Kuwata and K. Shigemoto