A critique on some aspects of GUP effective metric

Abstract

The generalized uncertainty principle (GUP) is a gravitational correction of Heisenberg’s uncertainty principle, which allows us to probe some features of quantum gravity even without the full theory. We are used to working with metric tensors in general relativity; they are convenient to have available when we wish to calculate physical quantities like Hawking temperature and black hole shadow. Various authors have tried to incorporate GUP into an effective metric that allows such calculations. In this note, I point out that some of these results are not correct due to working with series truncation rather than the full GUP-corrected expressions. Perhaps more importantly, we rely too much on heuristic arguments and lack a guiding principle in constructing the correct effective metric.

Tidal effects based on a GUP-induced effective metric

“…In this section, we briefly recapitulate Ong's idea [49] of getting an effective metric based on a GUP, and we study the metric's general properties. First, we begin with the most familiar form of a GUP given by…”

“…On the other hand, to incorporate the GUP into a metric, by following Ong's idea [49], one can consider a modified metric ansatz, without loss of generality, as…”

“…Various authors [41][42][43][44][45][46][47][48] have tried to incorporate GUPs into metrics, which we will call a GUP-induced effective metric. Very recently, Ong [49] has obtained a satisfying GUP-induced effective metric by emphasizing the importance of using the full GUP expression instead of just series expansions [44][45][46], which has some subtleties and shortcomings of undesired features.…”

30 years in: Quo vadis generalized uncertainty principle?

“…In its place, there are a number of heuristic approaches towards a minimal-length modification of the Schwarzschild Black Hole metric, namely an emergent-gravity scenario based on the GUP modified Black Hole entropy [161,297,389], a deformation of minisuperspace models in canonical QG [234,390,391] and a reparametrization of the Arnowitt-Deser-Misner (ADM) mass which, for small masses, mimics the Compton wavelength [198,392,393]. The proliferation of those different results further highlights the subtleties heuristic approaches entail, as reviewed in [394].…”

Modified Hawking radiation of Schwarzschild-like black hole in bumblebee gravity model

“…Moreover, the advent of the GUP has spurred investigations into the effects of quantum gravity on Hawking radiation. The incorporation of GUP into the analysis necessitates innovative calculation techniques, as emphasized in some remarkable studies [44][45][46][47][48][49][50]. This avenue opens up new paths for understanding the interplay between quantum mechanics and gravity in the context of Hawking radiation.…”