Charged rotating BTZ black holes in noncommutative spaces and torsion gravity

Abstract

We consider charged rotating BTZ black holes in noncommutative space by use of Chern-Simons theory formulation of 2 + 1 dimensional gravity. The noncommutativity between the radial and the angular variables is introduced through the Seiberg-Witten map for gauge fields, and the deformed geometry to the first order in the noncommutative parameter is derived. It is found that the deformation also induces nontrivial torsion, and the Einstein-Cartan theory appears to be a suitable framework to investigate the equations of motion. Though the deformation is indeed nontrivial, the deformed and the original Einstein equations are found to be related by a rather simple coordinate transformation. 1 We will review the noncommutativity deformation in more detail in Sec.2. 2 We have corrected the sign mistakes in f 2 and dϕ 2 parts in Ref. [16].

Dynamic noncommutative BTZ black holes

“…Here, {•, •} and F µν represent the anticommutator with respect to the conventional matrix product and the field strength for the gauge fields A µ , respectively. For the noncommutativity of the form (2.7), the correction terms to the gauge fields are given by [37] A…”

“…Noncommutativity plays a crucial role in many approaches of quantum gravity [4][5][6] as well as in several other branches of modern physics [7][8][9][10][11][12][13][14][15][16][17][18][19][20]. A particular interest is dispersed among different contexts of general relativity; such as wormholes [21] and black-holes [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”

“…Different scenarios of noncommutative black holes in diverse contexts have been explored over the years, such as the pair creation in a positive cosmological constant background [33], asymptotic quasinormal modes [26], Parikh-Wilczek tunneling [27], etc. The 2dimensional [32] and 3-dimensional [28,29,[34][35][36][37][38] studies of noncommutative black holes have also attracted a lot of interest in recent days.…”

“…Among various ways of implementing the noncommutativity in black holes, the most notable approaches include the application of the Seiberg-Witten (SW) map [3] on the Chern-Simons (CS) gauge theory [29,37] and the inclusion of noncommutative smearing by replacing point-like sources with a Gaussian [23,31,35] or a Lorentzian distribution [24,27,34]. In this article, we shall study charged BTZ black holes in noncommutative spaces by using both of the above approaches.…”

Noncommutative Correction to the Entropy of BTZ Black Hole with GUP

“…The process of massless scalar wave scattering by a noncommutative black hole via a Lorentzian smeared mass distribution has been explored in [16]. The thermodynamic properties of BTZ black holes in noncommutative spaces have been studied in [17][18][19][20].…”