Hayward Black Hole Solution in Non‐Metricity Gauss–Bonnet Gravity Coupled with a Scalar Field

Abstract In the present investigation, the quadratic formulation of , specifically , is employed incorporating a Gauss–Bonnet term coupled with a scalar field featuring a massless kinetic term and potential. This setup is applied to a spherically symmetric spacetime. An additional degree of freedom is offered by the emergent differential equations offer, which is leveraged to construct a model within this theoretical framework. The feasibility of circumventing ghost instabilities is explored by examining specific constraints tied to the parameters of the assumed black hole. It is shown that our solution always yields a ghost free theory either for large/small . The solution for the regular black hole involves three constants and is devoid of curvature singularities, which might offer a resolution to the information loss paradox commonly linked to black holes. The inclusion of the Gauss–Bonnet term is interpreted as a correction inspired by string theory, hinting at its possible role in resolving information loss. The thermodynamics and the first law of thermodynamics are shown to hold consistently, provided certain constraints are applied to avoid ghost instabilities.