Abstract
We investigate the massless scalar quasinormal modes (QNMs) of the noncommutative D-dimensional Schwarzschild-Tangherlini black hole spacetime in this paper. By using the Wentzel-Kramers-Brillouin (WKB) approximation method, the asymptotic iterative method (AIM) and the inverted potential method (IPM), we made a detail analysis of the massless scalar QNM frequencies by varying the general smeared matter distribution and the allowable characteristic parameters (k and θ) corresponding to different dimensions. It is found that the nonconvergence of the high order WKB approximation exists in the QNMs frequencies of scalar perturbation around the noncommutative D-dimensional Schwarzschild black holes. We conclude that the 3rd WKB result should be more reliable than those of the high order WKB method since our numerical results are also verified by the AIM method and the IPM method. In the dimensional range of 4≤D≤7, the scalar QNMs as a function of the different parameters (the noncommutative parameter θ, the smeared matter distribution parameter k, the multipole number l and the main node number n) are obtained. Moreover, we study the dynamical evolution of a scalar field in the background of the noncommutative high dimensional Schwarzschild-Tangherlini black hole.
Highlights
Motivated by string theory arguments [1], noncommutative spacetime has been studied extensively and is considered to be an alternative way to a quantum gravity
The basic idea of the noncommutative geometry is that the singularities in black holes at the origin can be avoided by the presence of spacetime minimal length: the point-like object on the classical commutative manifold should be replaced by a smeared object [2, 3]
It is known that noncommutative geometry inspired black holes contain stringy effects, where such an effect is similar in some sense to that of noncommutative field theory induced by string theory [5]
Summary
Motivated by string theory arguments [1], noncommutative spacetime has been studied extensively and is considered to be an alternative way to a quantum gravity. The method to noncommutative quantum field theory follows two distinct paths: one is based on the Weyl-Wigner-Moyal ⋆-product [2] and the other on coordinate coherent state formalism [3] Nicolini and his coworkers pointed out that the noncommutative effect is the inherent property of the manifold itself, not the superposition of the geometric structure. It is believed that QNMs is closely related to the Ads/CFT correspondence [29, 30] in string theory and loop quantum gravity [31, 32] All these motivated the extensive numerical and analytical studies of QNMs for different spacetime and fields around black holes [33–36]. A brief summary of the full text is presented
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