The GUP Effect on Tunneling of Massive Vector Bosons from The 2+1 Dimensional Black Hole

Ganim Gecim,Yusuf Sucu

doi:10.1155/2018/7031767

Abstract

In this study, the Generalized Uncertainty Principle (GUP) effect on the Hawking radiation formed by tunneling of a massive vector boson particle from the 2+1 dimensional new-type black hole was investigated. We used modified massive vector boson equation based on the GUP. Then, the Hamilton-Jacobi quantum tunneling approach was used to work out the tunneling probability of the massive vector boson particle and Hawking temperature of the black hole. Due to the GUP effect, the modified Hawking temperature was found to depend on the black hole properties, on the AdS3 radius, and on the energy, mass, and total angular momentum of the tunneling massive vector boson. In the light of these results, we also observed that modified Hawking temperature increases by the total angular momentum of the particle while it decreases by the energy and mass of the particle and the graviton mass. Also, in the context of the GUP, we see that the Hawking temperature due to the tunneling massive vector boson is completely different from both that of the spin-0 scalar and that of the spin-1/2 Dirac particles obtained in the previous study. We also calculate the heat capacity of the black hole using the modified Hawking temperature and then discuss influence of the GUP on the stability of the black hole.

Highlights

It was theoretically proved by Hawking that a black hole can emit thermal radiation as a result of quantum tunneling process of the particles created by the quantum fluctuation near the event horizon [1,2,3,4]
We investigate the quantum gravity effect on the tunneling massive vector boson from the new-type black hole in the context of the 2+1 dimensional New Massive Gravity
We found that the modified Hawking temperature depends on the black hole’s properties, and depends on the emitted spin-1 vector boson’s mass, energy, and total angular momentum

Summary

Introduction

It was theoretically proved by Hawking that a black hole can emit thermal radiation as a result of quantum tunneling process of the particles created by the quantum fluctuation near the event horizon [1,2,3,4]. To calculate the modified Hawking radiation in the GUP framework by HamiltonJacobi approach, Klein-Gordon equation for spin-0 particle, Dirac equation for spin-1/2 particle, and massive W∓-boson equation for spin-1 particle are modified [55,56,57] It shows that the modified Hawking temperature depends on properties of black hole, and on the properties of tunneling particle, such as mass, angular (orbital + spin) momentum, energy, charge [58,59,60,61,62,63,64,65,66,67,68,69,70,71].

Modified Vector Boson Equation

Tunneling of Vector Boson Particle from New-Type Black Hole

Summary and Conclusion