Black brane solutions of Einstein-scalar-Maxwell gravity and their holographic applications

Black hole solutions of Einstein (and Einstein-Maxwell) gravity coupled to scalar fields have acquired a growing interest and importance in recent years. This interest is motivated both by more classical" issues, as the problem of the uniqueness of classical black holes solutions (and related o-hair" theorems), and mainly by recent applications of the AdS/CFT correspondence, an holographic duality which allows to describe, starting from a gravitational theory, strongly coupled quantum field theories. In this thesis, we treat this topic both from a pure gravitational point of view and from the holographic perspective. In particular, we propose a general method for exactly solving, in some cases, the field equations of Einstein-scalar-Maxwell gravity, and present some new analytical and numerical solutions (we mainly focus on black brane solutions, i.e. solutions with a planar event horizon). Moreover, we discuss hyperscaling violation, a particular scaling behavior of free energy and entropy (as functions of the temperature), typical of some phase transitions of real condensed matter systems. Hyperscaling violation can be described, via AdS/CFT, starting from a gravitational solution with a particular symmetry. Finally, we perform some interesting results about the mass spectrum and stability of black brane solutions in a wide class of gravitational models. In particular, the thermodynamics of some solutions of these models provides important information about the possible existence of physicallyrelevant phase transitions in the dual field theories.