Quasinormal Modes and Choptuik Scaling in the Near Extremal Reissner-Nordstr{\"o} Black Hole

Abstract

We study quasinormal modes of massless scalar and fermion fields in the near extremal Reissner-Nordstr{\"o}m black hole, and relate them to Choptuik scaling form following a recently proposed analytic approach. For both massless cases, quasinormal modes are shown to be proportional to the black hole horizon and the Hawking temperature, and the critical exponents are the same, although for the fermionic case there are two possible discrete quasinormal modes. In addition, the critical exponent of the massive boson is also equivalent to that of the massless case. Finally, we discuss quasinormal modes and critical exponents in the other models, and obtain some different critical exponents between massless boson and massive one.