Abstract
Abstract We apply the generalized uncertainty principle to the thermodynamics of a small black hole. Here we have a black hole system with the UV cutoff. It is shown that the minimal length induced by the GUP interrupts the Gross–Perry–Yaffe phase transition for a small black hole. In order to see whether the black hole remnant takes place a transition to a large black hole, we introduce a black hole in a cavity (IR system). However, we fail to show the phase transition of the remnant to the large black hole.
Highlights
Hawking’s semiclassical analysis of the black hole radiation suggests that most information about initial states is shielded behind the event horizon and will not back to the asymptotic region far from the evaporating black hole [1]
We introduce the geometric means of UV and IR thermal quantities to study whether the phase transition to a stable large black hole is possible
The well-defined Gross-Perry-Yaffe (WGPY) phase transition occurs between hot flat space and a large black hole
Summary
Hawking’s semiclassical analysis of the black hole radiation suggests that most information about initial states is shielded behind the event horizon and will not back to the asymptotic region far from the evaporating black hole [1]. They have set the entropy to zero at the Planck scale This approach is not a complete work of the GUP effect on black hole thermodynamics. An important point is to know how the system of a black hole with positive heat capacity could be realized through the phase transition. This corresponds to the IR thermodynamics of the black hole in a cavity. We find that the black hole remnant is a thermodynamically stable object because of its positive heat capacity. We introduce the geometric means of UV and IR thermal quantities to study whether the phase transition to a stable large black hole is possible.
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