Zero, Normal and Super-radiant Modes for Scalar and Spinor Fields in Kerr-anti de Sitter Spacetime

Zero and normal modes for scalar and spinor fields in Kerr-anti de Sitter spacetime are studied as bound state problem with Dirichlet and Neumann boundary conditions. Zero mode is defined as the momentum near the horizon to be zero: $p_{\rm H}=\omega-\Omega_{\rm H}m=0$, and is shown not to exist as physical state for both scalar and spinor fields. Physical normal modes satisfy the spectrum condition $p_{\rm H}>0$ as a result of non-existence of zero mode and the analyticity with respect to rotation parameter $a$ of Kerr-anti de Sitter black hole. Comments on the super-radiant modes and the thermodynamics of black hole are given in relation to the spectrum condition for normal modes. Preliminary numerical analysis on normal modes is presented.