^{1}

^{1}

^{3}.

We investigate the generalized uncertainty principle (GUP) effect on the Hawking temperature for the 2 + 1-dimensional new-type black hole by using the quantum tunneling method for both the spin-1/2 Dirac and the spin-0 scalar particles. In computation of the GUP correction for the Hawking temperature of the black hole, we modified Dirac and Klein-Gordon equations. We observed that the modified Hawking temperature of the black hole depends not only on the black hole properties, but also on the graviton mass and the intrinsic properties of the tunneling particle, such as total angular momentum, energy, and mass. Also, we see that the Hawking temperature was found to be probed by these particles in different manners. The modified Hawking temperature for the scalar particle seems low compared with its standard Hawking temperature. Also, we find that the modified Hawking temperature of the black hole caused by Dirac particle’s tunneling is raised by the total angular momentum of the particle. It is diminishable by the energy and mass of the particle and graviton mass as well. These intrinsic properties of the particle, except total angular momentum for the Dirac particle, and graviton mass may cause screening for the black hole radiation.

Black hole radiation is theoretically very important phenomenon for researchers who attempt to merge the gravitation with the thermodynamics and the quantum mechanics [

The existence of a minimal observable length which can be identified by the order of the Planck scale is a characteristic of the candidate theories of quantum gravity, such as string theory, loop quantum gravity, and noncommutative geometry [

The GUP relations are of great help to understand the nature of a black hole since quantum effects are the essential effects near the event horizon of a black hole. Recently, to investigate the quantum effects under the GUP relations, the thermodynamics properties of various black holes have been studied by using the quantum tunneling process of particles with various spins [

The new-type black hole is one of the important results of the New Massive Gravity, which is 2 + 1-dimensional gravity and graviton in this theory has a mass [

The organization of this work is as follows: in Section

Using the GUP relations, the standard Dirac equation given in [_{3} radius defined as

To calculate the tunneling probability of a Dirac particle from the black hole, we use the following ansatz for the modified wave function:_{3} radius,

To investigate the quantum gravity effects on the tunneling process of the scalar particles from the black hole, by using the GUP relations, the standard Klein-Gordon equations are modified as follows:_{3} radius,

In this study, we investigated the quantum gravity effect on the tunneled both spin-0 scalar and spin-1/2 Dirac particles from new-type black hole in the context of 2 + 1-dimensional New Massive Gravity. For this, at first, using the GUP relations, we modified the Klein-Gordon and Dirac equations that describe the spin-0 scalar and spin-1/2 Dirac particles, respectively. Then, using the Hamilton-Jacobi method, the tunneling probabilities of the these particles are derived, and, subsequently, the corrected Hawking temperature of the black hole is calculated. We find that the modified Hawking temperature not only depends on the black hole’s properties but also depends on the emitted particle’s mass, energy, and total angular momentum. Also, it is worth mentioning that the modified Hawking temperature depends on mass of the graviton, that is, quantum particle which mediates gravitational radiation in the context of New Massive Gravity. As can be seen from (

In addition, we can summarize some important results as follows:

In (

However, in (

According to (

The new-type black hole is classified as six classes according to the signatures of the parameters

In the absence of the quantum gravity effect, that is,

Finally, in the context of GUP, we have seen that the graviton and the tunneling particle masses have an effect decreasing the Hawking temperature in both scalar and Dirac particle tunneling process. On the other hand, the total angular momentum has different effect on the Hawking temperature for a type of tunneling particle. For a scalar particle, it results in decrease in the temperature whereas it provides an increase in the temperature for a Dirac particle. These results show that the intrinsic properties of the particle, except total angular momentum for the Dirac particle, and graviton mass may cause screening for the black hole radiation.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by Akdeniz University, Scientific Research Projects Unit.