Remark on Remnant and Residue Entropy with GUP

In this article, close to the Planck scale, we discuss on the remnant and residue entropy from a Rutz-Schwarzschild black hole in the frame of Finsler geometry. Employing the corrected Hamilton-Jacobi equation, the tunneling radiation of a scalar particle is presented, and the revised tunneling temperature and revised entropy are also found. Taking into account generalized uncertainty principle (GUP), we analyze the remnant stability and residue entropy based on thermodynamic phase transition. In addition, the effects of the Finsler perturbation parameter, GUP parameter and angular momentum parameter on remnant and residual entropy are also discussed.Comment: 18 pages, 5 figures, 2 table

The Effects of Minimal Length, Maximal Momentum and Minimal Momentum in Entropic Force

In this paper, the modified entropic force law is studied by using a new kind of generalized uncertainty principle which contains a minimal length, a minimal momentum and a maximal momentum. Firstly, the quantum corrections to the thermodynamics of a black hole is investigated. Then, according to Verlinde's theory, the generalized uncertainty principle (GUP) corrected entropic force is obtained. The result shows that the GUP corrected entropic force is related not only to the properties of the black holes, but also to the Planck length and the dimensionless constants $\alpha _{\rm{0}}$ and $\beta _{\rm{0}}$. Moreover, based on the GUP corrected entropic force, we also derive the modified Einstein's field equation (EFE) and the modified Friedmann equation.Comment: 16 pages. arXiv admin note: substantial text overlap with arXiv:1604.0470