Grey-body factors of black holes

Grey-body factors describe the frequency-dependent transmission of fields through the effective potential generated by a black hole or another compact object. They convert the idealized thermal spectrum of Hawking radiation into the spectrum measured by an observer, determine absorption and scattering cross sections, and provide real-frequency observables complementary to quasinormal modes. In this review, we present a unified account of grey-body factors in black-hole physics and related systems. We formulate the scattering problem for asymptotically flat, de Sitter, and anti-de Sitter spacetimes, and discuss the connections between transmission coefficients, absorption cross sections, Hawking radiation, and ringdown. We also review methods for their computation and survey recent developments, including the correspondence between grey-body factors and quasinormal modes, their stability under deformations of the effective potential, wormhole transmission and superradiance, and their behavior in modified theories of gravity. Finally, we discuss the appearance of grey-body factors in gauge/gravity duality, where absorption probabilities in the bulk are related to correlation functions and transport coefficients in the boundary theory.