Generalized uncertainty principle from long-range kernel effects: The case of the Hawking black hole temperature

Abstract

We prove the existence of an analogy between spatial long range interactions which are of convolution-type introduced in non-relativistic quantum mechanics and the generalized uncertainty principle predicted from quantum gravity theories. As an illustration, black holes temperatures effects are discussed. It was observed that for specific choices of the moment's kernels, cold black holes may emerge in the theory.

Thermodynamics in a quantum corrected Reissner–Nordström–AdS black hole and its GUP-corrections

“…[51] It comes from a combination of quantum mechanics and general relativity, [20,48] which reveals that the basic physics laws may change under extreme conditions, such as extremely high energy [48,52,53] or extremely strong gravitational field. [8,[54][55][56][57][58] Applying the GUP to black hole physics, the corrections to the thermodynamic quantities are derived and the resolution of the difficulties of black hole thermodynamics is promoted (see Ref. [51] as a review and references therein).…”