Black hole corrections due to minimal length and modified dispersion relation

Abstract

The generalized uncertainty principles (GUP) and modified dispersion relations (MDR) are much like two faces for one coin in research for the phenomenology of quantum gravity which apparently plays an important role in estimating the possible modifications of the black hole thermodynamics and the Friedmann equations. We first reproduce the horizon area for different types of black holes and investigate the quantum corrections to Bekenstein-Hawking entropy (entropy-area law). Based on this, we study further thermodynamical quantities and accordingly the modified Friedmann equation in four-dimensional de Sitter-Schwarzschild, Reissner-Nördstrom and Garfinkle-HorowitzStrominger black holes. In doing this we applied various quantum gravity approaches. The MDR parameter relative to the GUP one is computed and the properties of the black holes are predicted. This should play an important role in estimating response of quantum gravity to the various metrictypes of black holes. We found a considerable change in the thermodynamics quantities. We find that the modified entropy of de-Sitter-Schwarzshild and Reissner-Nördstrom black holes starts to exist at a finite standard entropy. The Garfinkle-Horowitz-Strominger black hole shows a different entropic property. The modified specific heat due to GUP and MDR approaches vanishes at large standard specific heat, while the corrections due to GUP result in different behaviors. The specific heat of modified de-Sitter-Schwarzshild and Reissner-Nördstrom black holes seems to increase, especially at large standard specific heat. In the early case, the black hole cannot exchange heat with the surrounding space. Accordingly, we would predict black hole remnants which may be considered as candidates for dark matter.

Quantum-Corrected Two-Dimensional Horava-Lifshitz Black Hole Entropy

“…This seems to have the characteristic of theories that breakdown at the semi-classical regime. So, a minimum measurable length implies a major revision of quantum physics [39]. These approaches is precisely the GUP, as we see in section III.…”

“…In this section, we will consider the GUP and we will apply the Hamilton-Jacobi method in tunneling formalism to calculate the quantum-corrected Hawking temperature and entropy for a two-dimensional Horava-Lifshitz black hole. Hence, for the GUP we have [33][34][35][36][37][38][39]42] ∆x∆p…”

“…However, when determining the entropy by this method an ultraviolet cut-off must be inserted in the calculations to eliminate the divergence of states density near black hole horizon. On the other hand, considering models in which the Heisenberg uncertainty relation is modified the divergence that arise in the brick-wall model are eliminated [33][34][35][36][37][38][39]. For example, in one-dimensional space, we have the following modified Heisenberg uncertainty relation…”

Modified fermion tunneling from higher-dimensional charged AdS black hole in massive gravity

“…In Refs. [29][30][31][32][33][34][35][36][37], the authors studied the modified thermodynamic properties of black holes via the MDR; according to their results, the MRD has significant effect on the evolution of black holes, namely, it prevents black holes from total evaporation and leads to remnants. Meanwhile, it is believed that the MDR can modify the equation of motion of particles on the event horizon of black holes.…”

Nonlinear Schrödinger equation from generalized exact uncertainty principle

“…Let me only observe that the mathematical structure of (1) and its counterparts, lead by a straightforward optimization to the minimal measurable length [23], or in other cases to existence of minimal measurable momentum, minimal time interval or maximal measurable energy [28]. Such constrains, when considered, influence various domains of physics such as description of black holes [29] or Newton's laws of gravity [30].…”