General theory of relativity (or Lovelock extensions) is a dynamical theory; given an initial configuration on a space-like hypersurface, it makes a definite prediction of the final configuration. Recent developments suggest that gravity may be descr
ibed in terms of macroscopic parameters. It finds a concrete manifestation in the fluid-gravity correspondence. Most of the efforts till date has been to relate equilibrium configurations in gravity with fluid variables. In order for the emergent paradigm to be truly successful, it has to provide a statistical mechanical derivation of how a given initial static configuration evolves into another. In this essay, we show that the energy transport equation governed by the fluctuations of the horizon-fluid is similar to Raychaudhuri equation and, hence gravity is truly emergent.
Vacuum Einstein equations when projected on to a black hole horizon is analogous to the dynamics of fluids. In this work we address the question, whether certain properties of semi-classical black holes could be holographically mapped into properties
of (2 + 1)-dimensional fluid living on the horizon. In particular, we focus on the statistical mechanical description of the horizon-fluid that leads to Bekenstein-Hawking entropy. Within the paradigm of Landau mean field theory and existence of a condensate at a critical temperature, we explicitly show that Bekenstein-Hawking entropy and other features of black hole thermodynamics can be recovered from the statistical modelling of the fluid. We also show that a negative cosmological constant acts like an external magnetic field that induces order in the system leading to the appearance of a tri-critical point in the phase diagram.
We review aspects of the thermodynamics of black holes and in particular take into account the fact that the quantum entanglement between the degrees of freedom of a scalar field, traced inside the event horizon, can be the origin of black hole entro
py. The main reason behind such a plausibility is that the well-known Bekenstein-Hawking entropy-area proportionality -- the so-called `area law of black hole physics -- holds for entanglement entropy as well, provided the scalar field is in its ground state, or in other minimum uncertainty states, such as a generic coherent state or squeezed state. However, when the field is either in an excited state or in a state which is a superposition of ground and excited states, a power-law correction to the area law is shown to exist. Such a correction term falls off with increasing area, so that eventually the area law is recovered for large enough horizon area. On ascertaining the location of the microscopic degrees of freedom that lead to the entanglement entropy of black holes, it is found that although the degrees of freedom close to the horizon contribute most to the total entropy, the contributions from those that are far from the horizon are more significant for excited/superposed states than for the ground state. Thus, the deviations from the area law for excited/superposed states may, in a way, be attributed to the far-away degrees of freedom. Finally, taking the scalar field (which is traced over) to be massive, we explore the changes on the area law due to the mass. Although most of our computations are done in flat space-time with a hypothetical spherical region, considered to be the analogue of the horizon, we show that our results hold as well in curved space-times representing static asymptotically flat spherical black holes with single horizon.
