Quantum Gravity Correction to Hawking Radiation of the 2+1-Dimensional Wormhole

We carry out the Hawking temperature of a 2+1-dimensional circularly symmetric traversable wormhole in the framework of the generalized uncertainty principle (GUP). Firstly, we introduce the modified Klein-Gordon equation of the spin-0 particle, the modified Dirac equation of the spin-1/2 particle, and the modified vector boson equation of the spin-1 particle in the wormhole background, respectively. Given these equations under the Hamilton-Jacobi approach, we analyze the GUP effect on the tunneling probability of these particles near the trapping horizon and, subsequently, on the Hawking temperature of the wormhole. Furthermore, we have found that the modified Hawking temperature of the wormhole is determined by both wormhole’s and tunneling particle’s properties and indicated that the wormhole has a positive temperature similar to that of a physical system. This case indicates that the wormhole may be supported by ordinary (nonexotic) matter. In addition, we calculate the Unruh-Verlinde temperature of the wormhole by using Kodama vectors instead of time-like Killing vectors and observe that it equals to the standard Hawking temperature of the wormhole.

Black hole remnant and quantum tunneling corrections to the five-dimensional Myers–Perry black hole based on generalized uncertainty principle

Taking into account quantum gravity effect influenced by the generalized uncertain principle (GUP), via modified Dirac equation, we discuss the quantum gravity correction to fermion tunneling and the remnant in a five-dimensional Myers–Perry black hole. By analyzing the modified tunneling probability, we find that the emission spectrum is no longer pure thermal. Furthermore, it is worth emphasizing that the quantum gravity correction influenced by GUP prevents the black hole from evaporating totally, resulting in a black hole remnant.

Lorentz Invariance Violation and Modified Hawking Fermions Tunneling Radiation

Recently the modified Dirac equation with Lorentz invariance violation has been proposed, which would be helpful to resolve some issues in quantum gravity theory and high energy physics. In this paper, the modified Dirac equation has been generalized in curved spacetime, and then fermion tunneling of black holes is researched under this correctional Dirac field theory. We also use semiclassical approximation method to get correctional Hamilton-Jacobi equation, so that the correctional Hawking temperature and correctional black hole’s entropy are derived.

Massive fermions interacting via a harmonic oscillator in the presence of a minimal length uncertainty relation

We derive the relativistic energy spectrum for the modified Dirac equation by adding a harmonic oscillator potential where the coordinates and momenta are assumed to obey the commutation relation [Formula: see text]. In the nonrelativistic (NR) limit, our results are in agreement with the ones obtained previously. Furthermore, the extension to the construction of creation and annihilation operators for the harmonic oscillators with minimal length uncertainty relation is presented. Finally, we show that the commutation relation of the [Formula: see text] algebra is satisfied by the operators [Formula: see text] and [Formula: see text].

FORMULATION OF THE SPINOR FIELD IN THE PRESENCE OF A MINIMAL LENGTH BASED ON THE QUESNE–TKACHUK ALGEBRA

In 2006 Quesne and Tkachuk (J. Phys. A: Math. Gen.39, 10909, (2006)) introduced a (D+1)-dimensional (β, β′)-two-parameter Lorentz-covariant deformed algebra which leads to a nonzero minimal length. In this work, the Lagrangian formulation of the spinor field in a (3+1)-dimensional space–time described by Quesne–Tkachuk Lorentz-covariant deformed algebra is studied in the case where β′ = 2β up to first order over deformation parameter β. It is shown that the modified Dirac equation which contains higher order derivative of the wave function describes two massive particles with different masses. We show that physically acceptable mass states can only exist for [Formula: see text]. Applying the condition [Formula: see text] to an electron, the upper bound for the isotropic minimal length becomes about 3 ×10-13 m. This value is near to the reduced Compton wavelength of the electron [Formula: see text] and is not incompatible with the results obtained for the minimal length in previous investigations.