Constructing black hole solutions through gravitational decoupling approach in non-metric gravity

The main objective of this manuscript is to derive the new class of black hole solutions exhibiting exotic matter properties in the framework of f ( Q , T ) gravity, where Q is non-metricity and T the trace of the energy-momentum tensor. Using the extended gravitational decoupling approach, we separate the field equations into two sets, one for a seed source and another for an additional anisotropic source that introduces violations of the energy conditions. Three different analytical configurations emerge when a specific equation of state is implemented that relates the constituent components of the source. The solutions obtained show a variety of rich physical behaviors governed by a decoupling parameter. For the positive decoupling parameter values, the energy density throughout the entire configuration is positive, while in two of the three models the radial pressure becomes negative, a crucial characteristic that is usually found in the interiors of black holes. All extended solutions violate the energy conditions, verifying the existence of exotic matter interior to the spacetime geometry. The metric potentials of any configuration show no singularities of any sort at the event horizon ( r = 2 M ) , while the central curvature singularity at r = 0 is enclosed, maintaining the causal structure. Moreover, asymptotic analysis demonstrates that as r → ∞, all extended geometries gradually approach the condition of flat spacetime, confirming asymptotic flatness and providing a definitive closure to the analysis. This work establishes that f ( Q , T ) theory supports stable, asymptotically flat exotic compact objects, providing a new theoretical framework for horizonless alternatives to black holes.