# The GUP effect on tunnelling of massive vector bosons from the 2+1 dimensional black hole

## TL;DR

This paper investigates how the Generalized Uncertainty Principle (GUP) modifies Hawking radiation from a 2+1 dimensional black hole, revealing dependencies on particle properties and black hole parameters, and contrasting with other particle types.

## Contribution

It introduces a GUP-based modification to the vector boson tunneling equation and analyzes its impact on Hawking temperature and black hole stability.

## Key findings

- Modified Hawking temperature depends on black hole and particle properties.
- GUP increases temperature with particle angular momentum, decreases with energy and mass.
- Hawking temperature differs from scalar and fermion cases.

## 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, the AdS$_{3}$ 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 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 tunnelling massive vector boson is completely different from both that of the spin-0 scalar and 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.