Self-completeness and the generalized uncertainty principle

Abstract

The generalized uncertainty principle discloses a self-complete characteristic of gravity, namely the possibility of masking any curvature singularity behind an event horizon as a result of matter compression at the Planck scale. In this paper we extend the above reasoning in order to overcome some current limitations to the framework, including the absence of a consistent metric describing such Planck-scale black holes. We implement a minimum-size black hole in terms of the extremal configuration of a neutral non-rotating metric, which we derived by mimicking the effects of the generalized uncertainty principle via a short scale modified version of Einstein gravity. In such a way, we find a self-consistent scenario that reconciles the self-complete character of gravity and the generalized uncertainty principle. *

Thermodynamic phase transition based on the nonsingular temperature

“…This modified uncertainty relation will modify the classical geometry similar to the result in Ref. [39] so that the local temperature will be changed somehow near the horizon and, consequently, the thermodynamic behaviors of small black holes may be different from the the present results. This deserves further study, which we hope will appear in the future.…”

“…Note that modifications in the geometry could have a nontrivial effect on our analysis and an impact on the physics of small black holes. This was noticed in the GUP regime, which yields the corresponding GUP temperature, and the classical geometry should be changed according to the modification of the uncertainty relation [39]. Based on this fact, using the one-to-one correspondence between the GUP and the GUP temperature, a corresponding modified uncertainty relation, which is written as ∆x∆p + (2ℓ p /α)(2ℓ p /∆x) α ∆p ≥ 1, can also be derived straightforwardly from Eq.…”

“…Moreover, the stability of the remnant is not warranted since the heat capacity of the remnant approaches negative zero [34]. There have been extensive studies of the thermodynamics of black holes using the GUP temperature, [35][36][37][38], and the discussion for the above issues of GUP by deforming the Einstein-Hilbert action which leads to the formation of a zero temperature stable remnant [39].…”

Remnant mass and entropy of black holes and modified uncertainty principle

“…This idea, proposed first in [5], has led recently to a considerable amount of study in various areas of physics. For instance, the laws of black hole thermodynamics [6]- [8] has been investigated under this modification [9]- [12], quantum gravity corrections are computed in quantum systems (such as particle in a box, Landau levels and simple harmonic oscillator) [13]- [17], Planck scale corrections are obtained in the phenomena of superconductivity and quantum Hall effect [18] and its implications has been studied in cosmology [19], [20].…”

Quantum portrait of a black hole with Pöschl-Teller potential

“…This makes it quite unique as a toy model. Moreover, it is interesting to note that the Pöschl-Teller potential has appeared in a recent study [27] on the generalized uncertainty principle, which is another approach to reconcile gravity with quantum physics [28][29][30]. A non-relativistic model containing continuum states, however, is inconsistent, because most of the scattering modes would propagate with superluminal velocities.…”