Dynamic noncommutative BTZ black holes

TL;DR

This paper explores dynamic charged BTZ black holes in noncommutative spaces using two approaches, revealing non-static solutions and establishing bounds for stability, with thermodynamic analysis via tunneling formalism.

Contribution

It introduces the first non-static BTZ black hole solutions in noncommutative space and provides bounds for stability using two distinct noncommutative modeling approaches.

Findings

Discovery of non-static, non-stationary BTZ black holes in noncommutative spaces.

Establishment of bounds on noncommutative parameters for black hole stability.

Thermodynamic behavior analyzed through tunneling formalism.

Abstract

We have studied the charged BTZ black holes in noncommutative spaces arising from two independent approaches. First, by using the Seiberg-Witten map followed by a dynamic choice of gauge in the Chern-Simons gauge theory. Second, by inducing the fuzziness in the mass and charge by a Lorentzian distribution function with the width being the same as the minimal length of the associated noncommutativity. In the first approach, we have found the existence of non-static and non-stationary BTZ black holes in noncommutative spaces for the first time in the literature, while the second approach facilitates us to introduce a proper bound on the noncommutative parameter so that the corresponding black hole becomes stable and physical. We have used a contemporary tunneling formalism to study the thermodynamics of the black holes arising from both of the approaches and analyze their behavior within the context.