abstract: I will show that several families of non-homogeneous quantum walks can be viewed as discretizations of a spin 12 particle propagating in the curved space-time associated to a general relativistic gravitational field. In some cases, the fermion appears also coupled to an electric field. The result will be illustrated by the explicit construction of a quantum walk which simulates propagation around and inside a Schwarzschild black hole. General practical and fundamental implications will also be discussed.