  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.
