Gravitational decoupling and exotic matter effects in black hole solutions

In this paper, we generalize the Schwarzschild vacuum solution obtain new black hole configurations through the minimal geometric deformation technique in [Formula: see text] theory. Here, [Formula: see text] represents the non-metricity and [Formula: see text] denotes the trace of energy–momentum tensor. The presence of an extra source in this theory provides the anisotropy in the interior geometry. This method separates the radial component of the field equations into two distinct sets, one models an isotropic source and another one models an anisotropic source. The initial set represents the seed source (vacuum) and is characterized by the metric components of Schwarzschild spacetime. The second solution set derives from constraining the anisotropic extra source with a linear state equation. For specific values of the decoupling parameters, two extended solutions are obtained. The behavior of the matter comprising the additional source is studied by evaluating the energy conditions. It is observed that in both solutions, the additional source exhibits exotic properties, as it violates the energy conditions. We further investigate the asymptotic properties of both solutions by evaluating the deformed radial metric component. Only the solution corresponding to the conformally symmetric extra source maintained asymptotic flatness.