Noncommutative scalar quasinormal modes of the Reissner–Nordström black hole

Abstract

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.

Noncommutative field theory from an angular twist

“…In addition, τ is the extremality parameter, τ = r + −r − r + . For details see the reference [28]. In general, this condition cannot be solved analytically.…”

“…During this period black holes emit gravitational waves, which became accessible to an experimental inquiry since their first detection ever took place in the recent LIGO experiment [27]. In essence the purpose of the papers [28], [29], as well as of the present paper is to investigate this idea on the example of a realistic 4-dimensional black hole 1 . Specifically, besides assuming that quantum nature of spacetime may leave its trace in the QNM spectrum of a black hole, we also propose a specific model which enable us to sort out the trace of quantum spacetime and quantify analytically the associated signatures of spacetime noncommutativity.…”

“…In this way we ensure that the geometry remains intact by the deformation. For details of the construction the reader is referred to references [28], [29].…”

Noncommutativity and the weak cosmic censorship

“…It would be interesting to see what kind of physical effects would such quantum backreactions invoke, and we plan to investigate this more in the future. Finally, we note that the analysis carried out in this paper might be extended to 3+1 dimensional spacetime to investigate whether noncommutativity can dress a naked singularity in this more realistic situation and in case of a positive result, to study properties of the object obtained in this way [79][80][81].…”

Quasinormal modes of five-dimensional black holes in non-commutative geometry

“…In particular, it was shown that the gravitational wave signal from the event GW150914, detected by the LIGO and Virgo collaborations [36], could be used to obtain a bound on the scale of quantum fuzziness of noncommutative space-time [53]. QNMs of the BTZ black hole as well as four-dimensional black holes in noncommutative geometry have been studied in [54][55][56][57][58][59], while QNMs and gravitational radiation of standard higher-dimensional BHs have been studied in [60][61][62][63][64][65][66][67][68][69][70][71].…”