Axion Black Hole Solution in Non-Metricity Gravity

Document Type

Article

Publication Date

2-2026

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 (Formula presented.) and an axion–geometry coupling (Formula presented.), with temporal metric function (Formula presented.) and a nontrivial radial function (Formula presented.). 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 (Formula presented.) and determines the critical impact parameter, bending angle, and shadow size. Using the photon-sphere/eikonal correspondence, quasinormal-mode (QNM) frequencies are computed as (Formula presented.) where (Formula presented.) and (Formula presented.) is obtained from the curvature of the effective potential at (Formula presented.). The resulting spectrum is damped ((Formula presented.)), indicating linear stability, and displays a clear (Formula presented.) -dependence: increasing (Formula presented.) 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 ((Formula presented.)).

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