Solutions with a Flat Horizon in D Dimensions within the Cubic Form of f(Q) Gravity

Abstract

Given the AdS/CFT relationship, the study of higher-dimensional AdS black holes is extremely important. Furthermore, since the restriction derived from f(Q)’s field equations prevents it from deriving spherically symmetric black hole solutions, the result is either Q′=0 or fQQ=0. Utilizing the cylindrical coordinate system within the context the cubic form of f(Q) theory while imposing the condition of a coincident gauge, we establish the existence of static solutions in D-dimensions. The power-law ansatz, which is the most practical based on observations, will be used in this study, where f(Q)=Q+12γQ2+13γQ3−2Λ and the condition D≥4 are met. These solutions belong to a new solution class, the properties of which are derived only from the non-metricity Q modification, since they do not have a general relativity limit. We examine the singularities present in the solutions by calculating the non-metricity and curvature invariant values. In conclusion, we compute thermodynamic parameters such as Gibbs free energy, Hawking temperature, and entropy. These thermodynamic calculations confirm that our model is stable.