In the Dial-a-Ride-Problem (DARP) a fleet of vehicles provides shared-ride services to users specifying their origin, destination, and preferred arrival time. Typically, the problem consists of finding minimum cost routes, satisfying operational constraints such as time-windows, origin-destination precedences, user maximum ride-times, and vehicle maximum route-durations. This paper presents a problem variant for the DARP which considers the use of electric autonomous vehicles (e-ADARP). The problem covers battery management, detours to charging stations, recharge times, and selection of destination depots, along with classic DARP features. The goal of the problem is to minimize a weighted objective function consisting of the total travel time of all vehicles and excess ride-time of the users. We formulate the problem as a 3-index and a 2-index mixed-integer-linear program and devise a branch-and-cut algorithm with new valid inequalities derived from e-ADARP properties. Computational experiments are performed on adapted benchmark instances from DARP literature and on instances based on real data from Uber Technologies Inc. Instances with up to 5 vehicles and 40 requests are solved to optimality.