Greybody Factor for massive scalar field in charged black hole

TL;DR

This paper investigates how the mass of a scalar field affects the greybody factor in charged black holes, showing that higher mass reduces the probability of scalar wave transmission through the black hole potential barrier.

Contribution

It compares WKB and rigorous bound methods to analyze the inverse relationship between scalar field mass and greybody factor in Reissner-Nordström black holes.

Findings

Higher potential leads to lower greybody factor.

Both methods agree on the inverse relationship between mass and greybody factor.

Rigorous bounds are analytically calculable and applicable to wider parameter ranges.

Abstract

The greybody factor of a massive scalar field in the Reissner-Nordstr\"om 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 graybody 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.