Gravity and its wonders: braneworlds and holography

Abstract: Gravity is wonderful. The main goal of this thesis is to explore and discuss two aspects of gravity -- two wonders, which illustrate the richness of the theoretical gravitational landscape: braneworlds and holography. Each one of these topics is the core idea of the two parts of which the thesis consists. We begin by presenting gravity as a geometrical theory, then discuss extra dimensions and braneworld scenarios, to motivate the following derivation of the effective Einstein Field Equations on the brane. Afterward, we introduce the Randall--Sundrum model and derive the Minimal Geometric Deformation (MGD) method and its extension (EMGD), which are later on constrained by the classical tests of General Relativity. After this, we discuss black hole thermodynamics and the basic features of the AdS spacetime and black holes in it. We then present the basics of linear response theory and hydrodynamics, and discuss the AdS/CFT duality and its methods, which are employed in the calculation of the shear viscosity-to-entropy density ratio in different gravitational backgrounds, whose result is used to constrain the parameters of generalized 4D and 5D black branes. The relationship between the membrane paradigm and AdS/CFT is also presented. This is followed by a discussion of generalized actions and the violation of the Kovtun--Son--Starinets bound. Afterward, we present the fluid/gravity correspondence as well as an alternative to it in the context of soft hairy horizons. We finish the presentation with a summary of the main results and concluding remarks