Thermodynamic aspects of gravity

In this thesis we consider a scenario where gravitational dynamics emerges from the holographic hydrodynamics of some microscopic, quantum system living in a local Rindler wedge. We start by considering the area scaling properties of the entanglement entropy of a local Rindler horizon as a conceptually basic realization of the holographic principle. From the generalized second law and the Bekenstein bound we derive the gravitational dynamics via the entropy balance approach developed in [Jacobson 1995]. We show how this setting can account for the equilibrium and the nonequilibrium features associated with the gravitational dynamics and extend the thermodynamical derivation from General Relativity to generalized Brans-Dicke theories. We then concentrate on the possibility to define a version of fluid/gravity correspondence within the local Rindler wedge setting. We show how the hydrodynamical description of the horizon can be directly associated to a hydrodynamical description of the thermal fields. Because of the holographic behavior, the properties of the Rindler wedge thermal gauge theory are effectively encoded in a codimension one system living close to the Rindler horizon. In a large scale analysis, this system can be thought of as a fluid living on a codimension one stretched horizon membrane. This sets an apparent duality between the horizon local geometry and the fluid limit of the thermal gauge theory. Beyond the connection between the classical Navier-Stokes equations and a classical geometry, we discuss the possibility to realize such a duality at any point in spacetime by means of the equivalence principle. Given the shared local Rindler geometric setting, we eventually deal with the intriguing possibility to link the fluid/Rindler correspondence to the derivation of the gravitational field equations from a local non-equilibrium spacetime thermodynamics.