Analysis of black hole thermodynamics with a new higher order generalized uncertainty principle

Abstract

This research explores a unified expression for the black hole thermodynamics in the presence of a special generalized uncertainty principle (GUP). We have considered a heuristic analysis versus behavior of a particle which is absorbed by the black hole. Then we investigate the thermodynamic properties of the topological charged black hole under the consideration of GUP and we obtain the GUPcorrected temperature, entropy and heat capacity and we compare the behaviors of the usual temperature and the corrected temperature for the charged black hole in the spherical horizon case.

Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model

“…This equation cannot yet be compared with Eq. ( 38), since the term multiplying ψ(ζ ) depends explicitly on ζ , while in (38) it does not.…”

“…Implications of theories with a fundamental length are often addressed by deforming the Heisenberg Uncertainty Principle (HUP) in such a way as to accommodate a minimum uncertainty in position at Planck scale. The ensuing relation, commonly known as Generalized Uncertainty Principle (GUP), has been studied in a variety of contexts, ranging from quantum theory [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], to black hole physics [31][32][33][34][35][36][37][38][39][40][41][42][43][44] and cosmology [45,46]. Potential effects of a modified Heisenberg algebra have also been explored in graphene [47], where the minimal length is provided by the honeycomb lattice spacing.…”

Kinetic energy properties and weak equivalence principle in a space with generalized uncertainty principle

“…We would like also to note that in the case of deformed algebras leading to minimal length and maximal momentum [19,20,21,23,24] if relation (25) holds minimal length is proportional inversely to massh √ β =hγ/m and maximal momentum is proportional to mass 1/ √ β = m/γ. So, for macroscopic bodies one obtains reduction of the minimal length and increasing of the maximal momentum with respect to elementary particles.…”

“…To describe a space with minimal length and maximal momentum the following deformation [19,20] [24]. These algebras lead to existence of minimal length and maximal momentum which are proportional toh √ β and 1/ √ β, respectively [19,21,23,24]. We would like to stress that GUP leads to fundamental problems, among them are violation of the equivalence principle, violation of properties of the kinetic energy.…”

Thermodynamics of Schwarzschild black hole surrounded by quintessence with generalized uncertainty principle

“…It is worth noting that such an extension is not unique, therefore different GUP predictions exist. Each of the non-equivalent algebric deformations produces different new features, such as measurable minimal length, maximum momentum, etc.. [44,45] In the literature, we observe that the GUP is frequently employed in the papers that examine black hole thermodynamics [46][47][48][49][50][51][52][53][54][55][56][57][58][59]. However, to the best of our knowledge, no one has studied the black hole thermodynamics surrounded by the quintessence matter within the framework of the deformed Heisenberg algebra.…”