Quasinormal Modes and Choptuik Scaling in the Near Extremal Reissner-Nordström Black Hole

We study quasinormal modes of massless scalar and fermion fields in the near extremal Reissner-Nordström 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. PACS : 04.62.+v, 04.70.-s Typeset using REVTEX electronic address:[email protected] electronic address:[email protected] 1 One of the most exciting studies in gravitation is the gravitational collapse of infalling matters. When smooth initial data are slightly greater than those of critical ones, then the black hole formation appears, otherwise the matter fields eventually scattered below the critical values of initial data [1]. The dynamical behaviors are quite same and indistinguishable after certain time, and then the final state of the collapsing matter is determined by the initial data [2]. Since Bañados, Teitelboim, and Zanelli(BTZ) have found a nontrivial black hole solution in (2+1)-dimensional anti-de Sitter(AdS) spacetime which has a negative constant scalar curvature [3], it has been widely studied in diverse branches of theoretical physics, including gravity and string theory. Recently, in connection with a critical behavior of black hole formation in (2+1)-dimensional AdS spacetimes, several works have been done not only in numerical ways but also analytical ones. For a massless scalar field, critical behavior has been studied in Ref. [4] by supposing a scaling relation of an AdS black hole,