Abstract
The quasinormal modes of charged and uncharged massive scalar fields and also of charged Dirac fields against the background of a charged spherical black hole endowed with a scalar hair have been investigated. Special emphasis has been given to the case where negative scalar charge dominates over the electric charge of the black hole which mimics an Einstein-Rosen bridge. Except for the complete monotonic behaviour of the damping (imaginary part of the quasinormal frequency) against the charge of the black hole as opposed to the existence of a peak for the pure Reissner-Nordström case, the qualitative behaviour does not appreciably change due to the presence of scalar hair.
Highlights
After the dream of detecting gravity waves came true, and that too from a merger of two black holes [1], the importance of a thorough investigation of the quasinormal modes in connection with the black hole perturbations cannot perhaps be exaggerated
Quasinormal modes (QNM) for a Schwarzchild black hole has been studied by Vishveshwara [4] and by Davis, Ruffini, Press and Price [8]
Apart from a similar observation in the presence of a scalar hair as well, we note from Fig. 5f that such convergence of the imaginary part of the fundamental QN frequency occurs for any given value of the black hole electric charge, as the maximal value of the scalar charge is approached
Summary
After the dream of detecting gravity waves came true, and that too from a merger of two black holes [1], the importance of a thorough investigation of the quasinormal modes in connection with the black hole perturbations cannot perhaps be exaggerated These investigations started a long way back, through the work of Regge and Wheeler [2] and Vishveshwara [3,4]. 3, we briefly describe the continued fraction technique and discuss the QNMs for both uncharged and charged scalar fields close to a mutated RN black hole. The fifth and final section contains a summary and discussion on the results obtained As it is already mentioned, the work is done using the continued fraction method. We include a table showing the results of the two methods for one example as an “Appendix”
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