5th international istanbul scientific research congrees, İstanbul, Turkey, 14 - 15 August 2021, vol.1, pp.1-5
We study on two fermions system in the near horizon of Banados-Teitelboim-Zanelli (BTZ) black hole by using a fully-covariant two-body Dirac equation. Without considering any interaction between two fermions we solve the corresponding form of this two-body equation. By assuming the center-of-mass of this composite system is at rest at the near horizon of the BTZ black hole, we obtain exact solution of the corresponding equation. This solution gives the resonance modes of the considered composite system and accordingly we obtain Hawking temperature of the BTZ black hole. Then, we discuss the obtained resonance modes by comparing the previously pubished results in the literature.