Hawking radiation and graybody factor of slightly deformed Schwarzschild black holes

Abstract

We analyze the radiative properties of a general class of static and spherically symmetric black holes described by three independent shape functions, that encompass a broad family of regular and quantum-corrected geometries. We consider a minimally coupled massless scalar field, and derive the Hawking temperature and graybody factor for the different geometries. While the Hawking temperature is determined by the near-horizon geometry, the graybody factor depends on the scattering properties of the entire exterior spacetime, and therefore exhibits a richer dependence on the deformation parameters, frequency, and angular mode. Then we particularize to geometries that describe slight deformations of the Schwarzschild black hole, and obtain analytic expressions for the leading corrections to the graybody factor. Finally, we apply our results to several specific well-known black-hole models, including Reissner-Nordström, Bardeen, Hayward, Simpson-Visser, as well as geometries inspired by loop quantum gravity. In general, the deformations lead to colder horizons than Schwarzschild, and their effect on the graybody factor is frequency-dependent: the transmission of low-frequency modes is suppressed, whereas it is enhanced for high-frequency modes. This behavior is found for all but one of the geometries considered, which exhibits just the opposite trend. The analyzed modifications to the Hawking spectrum may therefore have relevant observational consequences, potentially providing signatures of deviations from the Schwarzschild geometry.