# The GUP effect on Hawking Radiation of the 2+1 dimensional Black Hole

## TL;DR

This paper examines how the Generalized Uncertainty Principle modifies Hawking radiation in a 2+1 dimensional black hole, revealing particle-dependent effects on temperature and tunneling probabilities.

## Contribution

It introduces a GUP-based approach to analyze Hawking radiation for scalar and Dirac particles in a 2+1D black hole, highlighting particle-specific differences.

## Key findings

- Hawking temperature depends on particle properties and black hole parameters.
- Tunneling probability varies between scalar and Dirac particles.
- GUP influences the Hawking radiation spectrum.

## Abstract

We investigate the Generalized Uncertainty Principle (GUP) effect on the Hawking radiation of the 2+1 dimensional Martinez-Zanelli black hole by using the Hamilton-Jacobi method. In this connection, we discuss the tunnelling probabilities and Hawking temperature of the spin-1/2 and spin-0 particles for the black hole. Therefore, we use the modified Klein-Gordon and Dirac equations based on the GUP. Then, we observe that the Hawking temperature of the scalar and Dirac particles depend on not only the black hole properties, but also the properties of the tunnelling particle, such as angular momentum, energy and mass. And, in this situation, we see that the tunnellig probability and the Hawking radiation of the Dirac particle is different from that of the scalar particle.