Noncommutative Correction to the Entropy of BTZ Black Hole with GUP

Abstract

We investigate the effect of noncommutativity and quantum corrections to the temperature and entropy of a BTZ black hole based on a Lorentzian distribution with the generalized uncertainty principle (GUP). To determine the Hawking radiation in the tunneling formalism, we apply the Hamilton-Jacobi method by using the Wentzel-Kramers-Brillouin (WKB) approach. In the present study, we have obtained logarithmic corrections to entropy due to the effect of noncommutativity and GUP. We also address the issue concerning stability of the noncommutative BTZ black hole by investigating its modified specific heat capacity.

Quasinormal modes and shadow of noncommutative black hole

“…By considering a Lorentzian mass distribution to introduce the noncommutativity, in 58 , we have explored the process of scattering and absorption of scalar waves through a noncommutative Schwarzschild black hole. Moreover, in 59 – 74 , the thermodynamics of the BTZ and Schwarzschild black holes in the noncommutative background has been investigated by using the WKB approach in tunneling formalism 75 – 77 . An advantage of using the Lorentzian distribution in analytical calculus has been investigated in 59 and 60 where logarithmic corrections for entropy and the condition for black hole remnant formation were obtained.…”

“…Moreover, in 59 – 74 , the thermodynamics of the BTZ and Schwarzschild black holes in the noncommutative background has been investigated by using the WKB approach in tunneling formalism 75 – 77 . An advantage of using the Lorentzian distribution in analytical calculus has been investigated in 59 and 60 where logarithmic corrections for entropy and the condition for black hole remnant formation were obtained.…”

Quantum Gravity Constraints on Fine Structure Constant from GUP in Braneworlds

“…Therefore, it is expected that on the Planck scale -that within the higher-dimensional framework is ∼ TeV -the effects of quantum gravity would manifest leading to correction to the Heisenberg uncertainty relation. Following these ideas, the most general GUP, including linear and quadratic contributions in momentum, can be expressed as [19],…”

“…Many works have employed the GUP formalism to the study of properties and possible corrections to several physical systems such as BTZ black hole [18,19] and acoustic black hole [20], approach to entropic nature of the gravitational interaction [21], study of the inflationary era [22], and also corrections for fine structure constant [23][24][25]. From a phenomenological point of view, experiments of gravitational and non-gravitational sources have been investigated, aiming to obtain constraints on the GUP deformation parameter [26][27][28][29][30][31][32][33][34][35].…”

EUP-corrected thermodynamics of BTZ black hole

“…Unlike the Schwarzschild and Kerr black holes, the BTZ black hole has a constant curvature which is not singular at origin [31]. For this reason, it has attracted attention and many studies have been conducted on it [32][33][34][35][36][37][38][39][40][41][42][43][44][45]. For example, Achúcarro and Ortiz revisited the BTZ solutions with dimensional reduction techniques [32].…”