Aiming to search for a signal of space-time noncommutativity, we study a quasinormal mode spectrum of the Reissner-Nordström black hole in the presence of a deformed space-time structure. In this context we study a noncommutative (NC) deformation of a scalar field, minimally coupled to a classical (commutative) Reissner-Nordström background. The deformation is performed via a particularly chosen Killing twist to ensure that the geometry remains undeformed (commutative). An action describing a noncommutative scalar field minimally coupled to the RN geometry is manifestly invariant under the deformed U(1) gauge symmetry group. We find the quasinormal mode solutions of the equations of motion governing the matter content of the model in some particular range of system parameters which corresponds to a near extremal limit. In addition, we obtain a well defined analytical condition which allows for a detailed numerical analysis. Moreover, there exists a parameter range, rather restrictive though, which allows for obtaining a QNMs spectrum in a closed analytic form. We also argue within a semiclassical approach that NC deformation does not affect the Hawking temperature of thermal radiation.

We consider a noncommutative field theory with space-time ⋆-commutators based on an angular noncommutativity, namely a solvable Lie algebra: the Euclidean in two dimension. The ⋆-product can be derived from a twist operator and it is shown to be invariant under twisted Poincaré transformations. In momentum space the noncommutativity manifests itself as a noncommutative ⋆-deformed sum for the momenta, which allows for an equivalent definition of the ⋆-product in terms of twisted convolution of plane waves. As an application, we analyze the λφ 4 field theory at one-loop and discuss its UV/IR behaviour. We also analyze the kinematics of particle decay for two different situations: the first one corresponds to a splitting of space-time where only space is deformed, whereas the second one entails a non-trivial ⋆-multiplication for the time variable, while one of the three spatial coordinates stays commutative. * dmarija@ipb.ac.rs

In our previous work [18] we constructed a model of a noncommutative, charged and massive scalar field based on the angular twist. Then we used this model to analyze the motion of the scalar field in the Reissner-Nordström black hole background. In particular, we determined the QNM spectrum analytically in the near-extremal limit. To broaden our analysis, in this paper we apply a well defined numerical method, the continued fraction method and calculate the QNM spectrum for a non-extremal Reissner-Nordström black hole. To check the validity of our analytic calculations, we compare results of the continued fraction method in the near extremal limit with the analytic results obtained in the previous paper. We find that the results are in good agreement. For completeness, we also study the QNM spectrum in the WKB approximation.

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