Noncommutative field theory from an angular twist

Abstract

Black hole (BH) perturbation is followed by a ringdown phase which is dominated by quasinormal modes (QNM). These modes may provide key signature of the gravitational waves. The presence of a deformed spacetime structure may distort this signal. In order to account for such effects, we consider a toy model consisting of a noncommutative charged scalar field propagating in a realistic black hole background. We then analyse the corresponding field dynamics by applying the methods of the Hopf algebra deformation by Drinfeld twist. The latter framework is well suited for incorporating deformed symmetries into a study of this kind. As a result, we obtain the BH QNM spectrum that, besides containing the intrinsic information about a black hole that is being analysed, also carry the information about the underlying structure of spacetime.

Noncommutativity and logarithmic correction to the black hole entropy

“…The differential calculus appropriate for the above context has been developed from an ordinary differential calculus through a deformation by means of the angular twist operator. The details of this can also be found in [29][30][31].…”

“…In our analysis, we shall use a NC scalar field in a classical RN background, coupled to a NC U(1) gauge field [29][30][31]. The NC algebra used in our model is the κ-deformed spacetime 1 [32][33][34][35][36], which is well known to be relevant for black hole physics [37][38][39] and cosmology [40].…”