Fermion quasinormal modes on modified RN background

Noncommutative (NC) geometry may open an alternative route to quantum gravity. We study the influence of the spacetime noncommutativity on the Dirac quasinormal modes in the modified Reissner-Nordstr\"om black hole spacetime. The framework for the latter study is provided by a certain effective model of gravity coupled to fermions which in itself encapsulates noncommutative deformation. This model describes a classical Dirac field coupled to a modified Reissner-Nordstr\"om geometry where the corresponding metric acquires an additional nonvanishing $r-\varphi$ component. As the earlier study shows, this model appears to be equivalent to a model of semiclassical NC gauge theory in which a NC gauge field is being coupled to a NC fermion field on the one side and the classical Reissner-Nordstr\"om background on the other. In comparison to the undeformed model where the Dirac field is coupled to the commutative Reissner-Nordstr\"om black hole, the numerical results show that the oscillation frequencies and magnitude of damping of the Dirac quasinormal modes change to an extent that cannot be neglected. In fact, the influence of spacetime noncommutativity is shown to produce features reminiscent of a Zeeman-like splitting in the effective potential and quasinormal-mode spectrum.