Three-dimensional charged black holes in f(Q) gravity

In this paper, we present new exact charged black hole solutions in (2+1) dimensions within the framework of [Formula: see text] gravity, where Q denotes the nonmetricity scalar. By considering a cubic [Formula: see text] form, we derive classes of charged and uncharged spherically symmetric solutions, and we identify conditions under which these reduce to the well-known Banados–Teitelboim–Zanelli (BTZ) black hole. Notably, our analysis reveals a novel charged solution that is asymptotically anti-de Sitter (AdS) but cannot be continuously deformed into a GR counterpart, and thus arising purely form the higher-order nature of the nonmetricity corrections. Furthermore, we explore the geometrical properties of the solutions, demonstrating the existence of multiple horizons and a softer central singularity compared to GR. Additionally, we calculate various thermodynamic quantities, such as Hawking temperature, entropy and heat capacity, with results confirming thermal stability. Finally, a detailed study of the geodesic motion and the effective potentials unveils stable photon orbits, as well as the effect of cubic nonmetricity corrections on orbital dynamics.