GUP effect on thermodynamical properties of the noncommutative rotating BTZ black hole

Abstract

<jats:p> In this paper, we investigated the quantum gravity effects on the thermal properties of the [Formula: see text]-dimensional noncommutative rotating Banados–Teitelboim–Zanelli (NCR-BTZ) black hole in the context of quantum tunneling of relativistic particles. These include Hawking temperature, the thermally local and global stability conditions, and the phase transitions. For this purpose, in the framework of the generalized uncertainty principle (GUP), we used the Hamilton–Jacobi approach to calculate the tunneling probability for a massive scalar, Dirac, and vector boson particles from the [Formula: see text]-dimensional NCR-BTZ black hole. We found that the modified Hawking temperature of the black hole depends on the black hole properties, on the tunneling particle properties, on the noncommutative parameter, and on the GUP parameter. Using the modified Hawking temperature, we calculated the modified heat capacity, and then we discussed the local thermodynamic stability conditions for the black hole. The black hole may undergo a first-type phase transition to become stable under the scalar particle tunneling whereas, it might undergoes both the first and the second-type phase transitions under the both Dirac and vector boson particles tunneling process. Furthermore, we calculated the Gibbs free energy of the black hole, and we investigated the global stability conditions. We observed that Hawking–Page phase transition may occur in the presence of the quantum gravity effect under the tunneling process of scalar, Dirac, and vector boson particles. In the context of quantum gravity effect, we also derived the modified equation of state to investigate the critical behavior of the commutative rotating BTZ black hole. Finally, we shown that Van der Waals-like phase transition may occur in the context of tunneling process of both Dirac and vector boson particle, whereas it may not occur for the tunneling of scalar particle. </jats:p>

Hawking radiation and entropy of a BTZ black hole with minimum length

“…Therefore, by solving the Einstein equations with these modifications, was determined the metric of a deformed Schwarzschild black hole due to noncommutativity. In addition, many papers have appeared in the literature suggesting different ways of introducing noncommutativity into Bañados-Teitelboim-Zanelli (BTZ) black holes [56][57][58][59][60][61][62][63][64][65][66]. Furthermore, the thermodynamic properties of noncommutative BTZ and noncommutative Schwarzschild black holes have been explored via Lorentzian distribution with GUP and logarithmic corrections for entropy have been obtained due to the noncommutativity effect [67,68].…”

Quasinormal modes and shadow of noncommutative black hole

“…By considering a Lorentzian mass distribution to introduce the noncommutativity, in [54], we have explored the process of scattering and absorption of scalar waves through a noncommutative Schwarzschild black hole. Moreover, in [55][56][57][58][59][60][61][62][63][64][65][66][67], the thermodynamics of the BTZ and Schwarzschild black holes in the noncommutative background has been investigated by using the WKB approach in tunneling formalism [68,69].…”

Noncommutative correction to the entropy of Schwarzschild black hole with GUP

“…In [34] the thermodynamic similarity between the noncommutative Schwarzschild black hole and the Reissner-Nordström black hole has been analyzed. By adopting the tunneling formalism the thermodynamics of noncommutative black holes has been investigated in [35][36][37][38][39][40][41][42][43][44]. In [45] by taking the mass density to be a Lorentzian smeared mass distribution the thermodynamic properties of noncommutative BTZ black holes has been studied and in [46,47] the process of massless scalar wave scattering by a noncommutative black hole was examined.…”