Emerging WGC from the Dirac particle around black holes

In this paper, we study the Dirac particle near the event horizon of the charged Banados-Teitelboim-Zanelli (BTZ) black hole and Reissner-Nordstrom (R-N) black holes to obtain its energy spectrum for discussing the weak gravity conjecture (WGC). The corresponding energy has both real and imaginary parts. We encounter the quasi-normal mode. Because the considered black holes have mass M and charge Q, this property allows us to examine the WGC using the energy spectrum with specific conditions. We attempt to investigate the WGC for these black holes by utilizing the Dirac particle energy spectrum obtained near charged black holes. Also, we impose conditions on the energy spectrum of particles for which the WGC holds for charged black holes, i.e. Q/M>1. To approve the WGC near the event horizon of black holes, we determine that the Dirac particle has a specified charge viz q=-1/2 omega and q=-1/ln(r+l) for R-N and charged BTZ black holes, respectively.