Greybody Factor for massive scalar field in charged black hole

The spectrum of Hawking radiation from black holes can be partially observed due to the spacetime curvature of the black hole behaving like a potential barrier. This spectrum can be described by arranging the Klein-Gordon equation on curved spacetime into the Regge-Wheeler equation. The transmission probabilities of Hawking radiation from this incident are called the greybody factor. In this work, the greybody factor of a massive scalar field in the Reissner-Nordström black hole is investigated using the Wentzel-Kramers-Brillouin (WKB) approximation and rigorous bound methods. As a result, we found that transmission probability and behavior of potential are directly related in such a way that the higher the potential the lower the greybody factor. Both methods achieve a similar conclusion, which states that the greybody factor and mass of the scalar field have an inverse relationship. This can be interpreted in a similar way in quantum mechanics, namely the scalar field with the higher mass will encounter a stronger interaction from the potential and then it is more difficult to penetrate through the potential barrier.