Greybody factors for a black hole in massive gravity

An exact solution was recently found in the massive gravity theory having the form of Schwarzschild-de Sitter (dS) black holes with some additional background fields. Hawking radiation will occur at the event and cosmological horizons having the blackbody spectrum, which will be modified by the geometry outside the black hole. In this paper, we study the greybody factors of a test scalar, considering its minimal coupling with the background geometry. The case of small black holes with a horizon radius much smaller than the cosmological dS radius is studied numerically. The case of near-extremal black holes with the horizon radius comparable to the cosmological dS radius is studied analytically. In addition, we considered the coupling of the test field with the background Stückelberg fields, which in turn leads to reductions in particle emission and some nontrivial features (resonances) in the greybody factors.