Noncommutative Scalar Quasinormal Modes of the Reissner Nordstr\"om Black Hole

TL;DR

This paper investigates how noncommutative space-time deformations influence the quasinormal mode spectrum of Reissner Nordström black holes, finding specific conditions where analytical solutions are possible and arguing that Hawking temperature remains unaffected.

Contribution

It introduces a novel noncommutative deformation of scalar fields in a black hole background, maintaining gauge and diffeomorphism invariance, and derives conditions for analytical and numerical quasinormal mode solutions.

Findings

Identified parameter ranges for quasinormal modes in a noncommutative setting.

Derived analytical conditions for quasinormal mode spectra.

Argued that noncommutativity does not alter Hawking temperature.

Abstract

Aiming to search for a signal of space-time noncommutativity, we study a quasinormal mode spectrum of the Reissner Nordstr\"om 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 Reissner Nordstr\"om background. Our model is thus semiclassical from the beginning and scalar field is in addition minimally coupled to U(1) gauge field. The deformation is performed via particularly chosen Killing twist to yield a geometrical form of the action, which maintains the diffeomorphism invariance manifest, as well as the invariance under a deformed 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 QNM 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.