An effective black hole remnant via infinite evaporation time due to generalized uncertainty principle

Abstract

We study a form of generalized uncertainty principle (GUP) that leads to vanishing quantum effect, i.e. ∆x∆p ∼ 0, at sufficiently high momenta. We find that such a GUP allows black holes to evaporate completely, however this process takes an infinite amount of time to achieve, resulting in a metastable remnant. We also discuss some connections between the proposed generalized uncertainty principle with other quantum gravity models.

A complementary third law for black hole thermodynamics

“…(1), we would find that there is no lower bound for black hole mass, so in principle the black hole can evaporate completely. However the final temperature is finite and nonzero [14,15], also see Fig. (1).…”

“…This is the case for the GUP-corrected black hole in [15] with negative GUP parameter α, since r h = 2M , the same as the usual Schwarzschild black hole; c.f. Eq.(4).…”

“…A denotes the horizon area, with the constant C incorporating the Boltzmann constant and the greybody factor. The effect of greybody factor, as well as the discreteness of the Hawking radiation (the sparsity [31][32][33]) can be ignored since their effects would result in an even longer evaporation time [15]. In the geometric optic approximation, it is the geometric optic cross section that goes into the Stefan-Boltzmann law, but we also absorb this correction into C, as it will not affect the qualitative behavior of the solution.…”

“…However, in [15], a more detailed study of the evaporation process reveals that the α < 0 GUP-corrected black hole actually takes an infinite amount of time to evaporate completely, so there is no need to resort to the aforementioned interpretation; the black hole simply continues to evaporate indefinitely (indeed its heat capacity is always negative and so it interacts thermodynamically with the environment), with temperature asymptotes to a finite nonzero value. This value is T * = 1/(4π |α|) [14,15] (note the typo in [15]). Thus even though black hole mass is not bounded below, the black hole behaves effectively as a meta-stable remnant at late times.…”

Minimal Length Effect on Thermodynamics and Weak Cosmic Censorship Conjecture in Anti-de Sitter Black Holes via Charged Particle Absorption

“…For a review of GUP, see [47]. GUP is one of the simplest models of effective quantum gravity, and many interesting results in the study of black hole physics have been produced [48][49][50][51][52][53][54][55][56][57][58][59]. Specifically, the authors of [60] discussed the effect of quantum gravity on the weak cosmic censorship conjecture and showed that the second law of thermodynamics and the cosmic censorship conjecture are violated owing to the rainbow effect.…”