Black Hole Thermodynamics and Generalized Uncertainty Principle with Higher Order Terms in Momentum Uncertainty

Abstract

We study the modification of thermodynamic properties of Schwarzschild and Reissner-Nordström black hole in the framework of generalized uncertainty principle with correction terms up to fourth order in momentum uncertainty. The mass-temperature relation and the heat capacity for these black holes have been investigated. These have been used to obtain the critical and remnant masses. The entropy expression using this generalized uncertainty principle reveals the area law up to leading order logarithmic corrections and subleading corrections of the form 1/ . The mass output and radiation rate using Stefan-Boltzmann law have been computed which show deviations from the standard case and the case with the simplest form for the generalized uncertainty principle.

Thermodynamics of the Schwarzschild and Reissner–Nordström black holes under the Snyder–de Sitter model

“…We can see in the absence of correction due to EGUP, the relationship obtained for entropy reduces to the semiclassical Bekenstein-Hawking entropy for the Schwarzschild black hole as S = A 4 [41]. Also we can investigate the behavior of the corrected black hole entropy versus different characteristics of Schwarzschild black hole.…”

“…We utilize the Schwarzschild radius of the black hole as [41] where G is the Newton's universal gravitational constant and we can consider the position uncertainty of a particle as the order of the Schwarzschild radius of the black hole near the horizon of the black hole…”

“…8πκT 2 obtained in Refs. [29] and [41]. In order to calculate the entropy S in terms of the black hole mass, a useful heuristic method for a particle which is captured by the black hole has been presented in Ref.…”

“…In Ref. [41] the thermodynamics of Schwarzschild and Reissner-Nordström (RN) black holes in the framework of GUP with correction terms up to fourth order in momentum uncertainty have been investigated and this has led to the existence of a remnant mass thereby preventing the complete evaporation of the black hole. Also it has been observed that analytical expressions for these masses can be obtained for terms of the order of ( p) 8 in the momentum uncertainty.…”

“…In [41], the entropy for the Schwarzschild black hole for (h = c = G = κ = 1) is defined as S = A 4 . Also, from consistency of thermodynamic information of the black hole in absence of EGUP with the semi-classical case, we can define ξ = 4 ln 2 [21].…”