GUP black hole remnants in quadratic gravity

Iberê Kuntz,Roldão da Rocha

doi:10.1140/epjc/s10052-020-8049-9

Abstract

The Hawking radiation of static, spherically symmetric, asymptotically flat solutions in quadratic gravity is here scrutinized, in the context of the generalized uncertainty principle (GUP). Near-center and near-horizon Frobenius expansions of these solutions are studied. Their Hawking thermal spectrum is investigated out of the tunnelling method and the WKB procedure. Computing the Hawking flux of these black hole solutions shows that, for small black holes and for a precise combination of the GUP parameter and the parameters that govern the gravitational interaction in quadratic gravity, the black hole luminosity can vanish. This yields absolutely stable mini black hole remnants in quadratic gravity.

Highlights

Black hole thermodynamics has been occupying a prominent spot in physics in the last five decades, since the Bekenstein’s conjecture was posed, asserting that black hole physics has a close relationship with the laws of thermodynamics [1]
Taking into account generalized uncertainty principle (GUP) effects, we investigated the particles tunnelling in the background of static, spherically symmetric, asymptotically flat solutions in quadratic gravity
The bounds on the parameters of the near-origin black hole solutions obtained are displayed in Eqs. (44)–(46), whereas the constraints on the parameters of the near-horizon black hole solutions are shown in Eqs. (55)–(57)

Summary

Introduction

Black hole thermodynamics has been occupying a prominent spot in physics in the last five decades, since the Bekenstein’s conjecture was posed, asserting that black hole physics has a close relationship with the laws of thermodynamics [1]. Notwithstanding the fact that GUP effects in black hole remnants were already extensively studied in the literature [28,29,30,31,32,33], a detailed analysis involving GUP in higher-derivative gravity is lacking, despite a recent development [34]. Using the semiclassical approach of the WKB approximation, the tunnelling rate and the black hole luminosity will be calculated, showing that for appropriate parameters of the black hole solution in higher-derivative gravity the black hole luminosity equals zero.

Static spherically symmetric solutions in higher-derivative gravity

B Btt 2B2

Concluding remarks