Analytic Primary Scalar hair Charged Black Holes and their Thermodynamics in AdS Space in D Dimensions

Abstract

Black holes are the simplest and yet the most mysterious objects in our Universe that have brought to light strong hints of a profound and fundamental connection between gravity, thermodynamics, and quantum theory. Classical black holes are believed to follow the famous no-hair theorem, which states that black holes are characterized by only three parameters: their mass, charge, and angular momentum. The main aim of this thesis is first to present and discuss new families of primary hair-charged black hole solutions in asymptotically anti–de Sitter (AdS) spaces in various dimensions and then study their thermodynamic properties. For this purpose, we consider the Einstein-Maxwell-scalar gravity system that carries the nontrivial coupling between the scalar and Maxwell fields. We analytically solve the coupled Einstein-Maxwell-scalar field equations and obtain exact hairy charged black hole solutions in various dimensions. The analytic hairy black hole solutions are obtained for various horizon topologies. This includes planar, spherical, and hyperbolic horizon topologies. The thesis work carried out with reference to hairy black holes provides several interesting novel results and observations. Particularly, the constructed hairy solutions exhibit many desirable features, including the well-behaved nature of the scalar field and curvature scalars everywhere outside the horizon. In addition, analytic expressions of regularized action, stress tensor, conserved charges, and free energies are obtained. We analyze the thermodynamics of the hairy black holes in canonical and grand-canonical ensembles and find that the scalar hair significantly modifies the thermodynamic structure of the black hole. This includes the occurrence of small/large black hole phase transition not only in the grand-canonical ensemble but also in lower three-dimensional gravity systems. Similarly, there also occurs an interesting hairy/nonhairy phase transition, with thermodynamically preferred and stable hairy phases at low temperatures. Moreover, we also analyze the dynamical stability of the massless scalar field perturbation in the constructed hairy backgrounds and find that the scalar perturbations are stable. Our analysis further suggests that the corresponding scalar quasi-normal modes can probe the small/large hairy black hole phase transition.