# Greybody factor for black holes in dRGT massive gravity

## TL;DR

This paper investigates the greybody factor for black holes within dRGT massive gravity, deriving bounds and comparing methods to understand how potential structures influence Hawking radiation escape probabilities.

## Contribution

It provides the first calculation of the rigorous bound on the greybody factor for dRGT black holes and compares it with the matching technique results.

## Key findings

- Higher potentials lead to lower bounds on the greybody factor.
- The rigorous bound is confirmed as a true lower bound compared to the matching technique.
- Potential structures significantly influence the greybody factor bounds.

## Abstract

In general relativity, greybody factor is a quantity related to the quantum nature of a black hole. A high value of greybody factor indicates a high probability that Hawking radiation can reach infinity. Although general relativity is correct and has been successful in describing many phenomena, there are some questions that general relativity cannot answer. Therefore, general relativity is often modified to attain answers. One of the modifications is the `massive gravity'. The viable model of the massive gravity theory belongs to de Rham, Gabadadze and Tolley (dRGT). In this paper, we calculate the gravitational potential for the de Sitter black hole and for the dRGT black hole. We also derive the rigorous bound on the greybody factor for the de Sitter black hole and the dRGT black hole. It is found that the structure of potentials determines how much the rigorous bound on the greybody factor should be. That is, the higher the potential, the lesser the bound on the greybody factor will be. Moreover, we compare the greybody factor derived from the rigorous bound with the greybody factor derived from the matching technique. The result shows that the rigorous bound is a true lower bound because it is less than the greybody factor obtained from the matching technique.