Corrected Black Hole’s Thermodynamics and Tunneling Radiation with Generalized Uncertainty Principle and Modified Dispersion Relation

Abstract

Although the tunneling approach is well established for black hole radiation, much works have been done to support the extension of this approach to more general situations. In this article the Parikh-Kraus-Wilczek tunneling proposal of black hole radiation is considered. The black hole thermodynamics and tunneling radiation are studied, based on both, the generalized uncertainty principle and the modified dispersion relation analysis. It is shown that entropy, temperature and the original Parikh-Kraus-Wilczek tunneling radiation calculation receives new corrections. it has been shown that the results of this two alternative approaches are identical if one uses the suitable expansion coefficients.

Black hole evaporation and its remnants with the generalized uncertainty principle including a linear term

“…At the same time, since there is no scale factor μ in the temperature expression obtained when α → 0, regardless of the value of μ, the temperature expression can be simplified to the semi-classical Hawking temperature without considering quantum correction. For convenience, according to [34] take: Integrate equation (24), an expression S L for entropy in logarithmic form is obtained: We observe that there are logarithmic terms in the expression of entropy, which is consistent with numerous studies [11,13,26,29,[34][35][36]39].…”

“…People have also modified the traditional Heisenberg uncertainty principle, which contradicts the existence of a minimum length, and proposed the generalized uncertainty principle (GUP). After its proposal, the GUP was quickly applied to various areas of physics such as gravitational corrections for quantum systems [7][8][9][10], corrections to the thermodynamics of black holes [11][12][13][14][15][16][17], and cosmology [18,19]. Additionally, the positive and negative GUP parameters have sparked numerous discussions: rainbow gravity corrections to the black hole information flux and Hawking radiation sparsity [20], the modification of special relativity [21], and the negative parameter of the GUP to recover the Chandrasekhar's limit [22], etc., argue that the negative parameter is applicable to a specific model.…”

Minimal Length Scale Scenarios for Quantum Gravity

“…It has also been argued that taking into account the GUP may give rise to black-hole remnants [2], a possibility that has been explored in many follow-up works, e.g., [87,243,315]. Corrections to the thermodynamical properties of a Schwarzschild black hole have been looked at in [22,321,100,214,217], the Reissner-Nordström black hole has been considered in [319], and black holes in anti-de Sitter space in [280,281,61]. Black-hole thermodynamics with a GUP has been studied in [201,237,54,186], the thermodynamics of Kerr-Newman black holes in [315], and the entropy of a charged black hole in f (R) gravity in [273].…”