Black-hole stability in non-local gravity

5 pags., app. -- Open Access funded by Creative Commons Atribution Licence 4.0We prove that Ricci-flat vacuum exact solutions are stable under linear perturbations in a new class of weakly non-local gravitational theories finite at the quantum level.G.C. is under a Ramón y Cajal contract and thanks SUSTech for the kind hospitality during the writing of this work. G.C. and L.M. are supported by the MINECO I+D grants FIS2014-54800-C2-2-P and FIS2017-86497-C2-2-P.Peer Reviewe