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

摘要

Normal modes, quasi-normal modes and super-radiant modes are studied toclarify the total dynamics for complex scalar fields in Kerr anti-de Sitterblack hole spacetime. Orthonormal relations and quasi-orthonormal relations areobtained for normal modes and quasi-normal modes. Mode expansions are done andthe conserved quantities are studied. Any modes are shown to be separated intotwo groups, physical modes and unphysical modes, by the zero mode line. Zeromodes themselves do not exist as normalizable modes with the correct boundarycondition. The allowed physical modes exclude the super-radiant instabilitymodes in rotating black hole spacetime. The result is consistent with theco-rotating frame consideration.