Comparison of approaches to quantum correction of black hole thermodynamics

Abstract

There are several approaches to quantum gravitational corrections of black hole thermodynamics. String theory and loop quantum gravity, by direct analysis on the basis of quantum properties of black holes, show that in the entropy-area relation the leading order correction should be of log-area type. On the other hand, generalized uncertainty principle(GUP) and modified dispersion relations(MDRs) provide perturbational framework for such modifications. Although both GUP and MDRs are common features of all quantum gravity scenarios, their functional forms are quantum gravity model dependent. Since both string theory and loop quantum gravity give more reliable solution of the black hole thermodynamics, one can use their results to test approximate results of GUP and MDRs. In this paper, we find quantum corrected black hole thermodynamics in the framework of GUP and MDR and then we compare our results with string theory solutions. This comparison suggests severe constraints on the functional form of GUP and MDRs. These constraints may reflect characteristic features of ultimate quantum gravity theory.

Generalized uncertainty principle, modified dispersion relations and the early universe thermodynamics

“…As has been indicated, there are severe constraints on the functional form of MDR which these constraint are motivated when one compares black hole entropy-area relation in different points of view [15,21]. In this case we should set α 1 = 0 which leads to a = 0.…”

“…There are some conceptual relations between GUP and MDRs. These possible relations have been studied recently [14,15].…”

Black hole corrections due to minimal length and modified dispersion relation

“…Anomalies in ultra-high cosmic rays and γ-TeV events at LHC, may be explained by modification in the dispersion relation [41][42][43][44][45][46][47][48][49][50].…”

“…In additional to that, the possibility that the relation connecting energy and momentum in Special Relativity (SR) may be modified at Planck scale because of the threshold anomalies of ultra-high energy cosmic ray (UHECR). This enters the literature as Modified Dispersion Relations (MDRs) [41][42][43][44][45][46][47][48][49][50] and can provide new sensitive tests for SR. Successful searches would reveal a surprising connection between particle physics cosmology [37][38][39][40].…”

Quantum tunneling from a high dimensional Gödel black hole

“…Recently, incorporating quantum gravity effects into black hole's physics, generalized uncertainty principle (GUP) with a minimal measurable length has attracted a lot of interest [19][20][21][22][23][24][25][26]. A minimal observable length arises naturally when incorporating gravity into quantum field, which also leads to a modification of original uncertainty principle.…”