Comparison of Approaches to Quantum Gravitational Corrections on the Reissner-Nordström-de Sitter Black Hole Tunneling Radiation

Abstract

Although the tunneling approach is fully established for black hole radiation, much work has been done to support the extension of this approach to more general settings. In this letter the Parikh-Kraus-Wilczeck tunneling proposal of black hole tunneling radiation is considered. The Reissner-Nordström-de Sitter black hole thermodynamics is studied according to the generalized uncertainty principle and the modified dispersion relation analysis. It is shown that entropy, temperature and the original Parikh-Kraus-Wilczek calculations of the black hole tunneling probability receive new corrections. The results are compared and it is shown that these two alternative approaches lead to the same results if one uses the suitable expansion coefficients.

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

“…It is shown that usual uncertainty principle receives a modification at the microphysics regime [36][37][38][39][40][41][42][43][44][45],…”

Thermodynamics of Vaidya-Bonner-de Sitter space time based on the generalized space-time uncertainty

“…They showed that, based on the generalized uncertainty principle, the hawking temperature receives a correction. Other derivations of this proposal are obtained in (Han et al 2008;Farmany et al 2008;Shu and Shen 2008;Fu et al 2008;Kim and Park 2007;Nouicer 2007;Ren and Zhang 2006;Xiang 2006;Farmany et al 2009;Farmany et al 2011aFarmany et al , 2011bFarmany 2009b, 2009b;Dehghani and Farmany 2010).…”

Hawking Effect with Generalized Uncertainty Principle and Modified Dispersion Relations in de Sitter-Schwarzschild Black Hole

“…It is shown that usual uncertainty principle receives a modification at the microphysics regime [38][39][40][41][42][43][44][45][46][47] x ≥ p + αL 2 P p , (3.1) where L P = G c 3 is the Planck length. The term αL 2 P p in (3.1) shows the gravitational effects on the usual uncertainty principle, in which α is a constant coefficient.…”

“…By modeling the black hole as a black box with linear size equal to twice it's radius r + the uncertainty in the position of an emitted particle by the Hawking effect is [46][47][48][49] x = 2r…”