An innovative black hole solution and thermodynamic properties in higher-order curvature gravity with a scalar field

A spherically symmetric black hole solution defined by the gravitational mass is explored in higher-order curvature gravity associated with a scalar field. It is demonstrated that the singularities of the curvature invariants will be far weaker around the central region of the black hole than those in general relativity, owing to the effect originating from higher-order curvatures with the coupling to a dynamical scalar field. Furthermore, thermodynamic properties and the Davies-type phase transition of the black hole are investigated for Barrow entropy with a quantum effect of gravitation. It is found that both the quasi-local energy and Gibbs free energy are positive, and the black hole can hence be stable on the smooth horizon surface. In addition, by analyzing the geodesic deviation, the stability conditions of the black hole are explicitly shown.