Axion Black Hole Solution in Non‐Metricity Gravity

Abstract

Abstract A static, spherically symmetric black hole solution in symmetric teleparallel (non‐metricity) gravity sourced by an axion field is constructed. Starting from the modified field equations, exact configurations are obtained characterized by the mass and an axion–geometry coupling , with temporal metric function and a nontrivial radial function . The horizon structure and thermodynamics (temperature, entropy, heat capacity) are analyzed, showing regular outer‐horizon behavior across the explored parameter ranges. The dynamics of test particles and light are studied via the effective potential, from which the conditions for circular orbits and the photon sphere are derived; the latter satisfies and determines the critical impact parameter, bending angle, and shadow size. Using the photon‐sphere/eikonal correspondence, quasinormal‐mode (QNM) frequencies are computed as where and is obtained from the curvature of the effective potential at . The resulting spectrum is damped (), indicating linear stability, and displays a clear ‐dependence: increasing raises both the oscillation frequency and the damping rate. Altogether, the axion–non‐metricity deformation leaves correlated signatures in the thermodynamics, orbital structure, lensing/shadow observables, and ringdown behavior, offering potential observational tests relative to the Schwarzschild limit ().