Black Holes, Holography and the Dark Universe

We investigate various aspects of gravity with the aim to shed light on the deep relation between the infrared and ultraviolet regimes of gravitational interaction. We focus on black holes, holography, the emergent properties of spacetime and gravity itself and its relation to the behaviour of gravity at galactic scales. In the first part of the thesis, we study geometrical, thermodynamical and holographic properties of two dimensional and higher dimensional black holes in Anti-de Sitter spacetime in the context of the AdS/CFT correspondence. We discuss two different applications of the AdS/CFT correspondence: the shear viscosity to entropy density ratio for five dimensional charged Reinssner-Nordström and Gauss-Bonnet black branes and black holes and quantum holographic properties of two dimensional dilaton gravity. For black branes we find an universal thermodynamical behaviour and a monotonic flow from the UV to the IR of the shear viscosity to entropy density ratio as a function of the temperature. In the black hole case we find an interesting connection between phase transitions in the bulk and a hysteretical behaviour of the shear viscosity to entropy density ratio in the dual quantum field theory. For two dimensional dilaton gravity we show that the pattern of conformal symmetry breaking is crucial to understand the microscopic properties of two dimensional dilaton black holes. In the second part of the thesis we describe the emergent laws of gravity in a corpuscolar picture and derive the implications of our emergent gravity scenario at galactic scales. We first describe spacetime as a Bose-Einstein condensate of gravitons, then we demonstrate that, without assuming the existence of exotic matter, the phenomenology commonly attributed to dark matter at galactic scales (the flattening of rotational curves) can be described as a reaction of the cosmological condensate to the presence of localized baryonic matter. We show how this corpuscolar picture of gravity allows for an effective description in terms of general relativity sourced by an anisotropic fluid. Finally, using a more conservative approach, we derive an exact, analytic, static, spherically symmetric, four-dimensional solution of minimally coupled Einstein-scalar gravity, sourced by a scalar field which could be considered as a possible dark matter candidate.