Bouncing Universe Scenario via Black Hole Solutions in 3D <i>F</i> ( <i>Q,T</i> ) Gravity

This paper presents a novel investigation of a non-singular cosmological bounce emerging from black hole inspired solutions within the framework of three-dimensional [Formula: see text]([Formula: see text]) gravity, a recently developed extension of symmetric teleparallel geometry coupling non-metricity [Formula: see text] and the matter trace [Formula: see text]. By adopting a dynamical metric that incorporates both temporal and radial dependencies near the black hole horizon, we analytically derive and numerically examine the evolution of the scale factor, pressure, energy density, and equation of state parameter in the weak-field limit. The results demonstrate a smooth transition between contracting and expanding phases without curvature singularities, confirming that the [Formula: see text]([Formula: see text]) coupling can naturally violate the strong energy condition and sustain a cosmological bounce without invoking exotic fields or quantum corrections. Moreover, the model predicts bounded metric perturbations and oscillatory behavior of the equation of state parameter [Formula: see text]([Formula: see text]), implying an inherent cyclic or quasi-periodic universe consistent with recent theoretical and observational trends in modified gravity cosmology. The study introduces, for the first time, a consistent 3D realization of the bouncing universe scenario based on black hole type geometries in [Formula: see text]([Formula: see text]) gravity, thereby providing an innovative and up to date perspective that bridges lower-dimensional gravity, black-hole thermodynamics, and cyclic cosmological evolution.