Greybody factor for massive scalar field in charged black hole

Abstract

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. We found that the transmission probability and behavior of the 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 the 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. The rigorous bound has the advantage of not only being possible to calculate analytically, but also being applicable to a wider range of parameter values compared to the standard WKB approximation.