There is a compelling connection between equations of gravity near the black-hole horizon and fluid-equations. The correspondence suggests a novel way to unearth microscopic degrees of freedom of the event horizons. In this work, we construct a micro
scopic model of the horizon-fluid of a 4-D asymptotically flat, quasi-stationary, Einstein black-holes. We demand that the microscopic model satisfies two requirements: First, the model should incorporate the near-horizon symmetries (S1 diffeomorphism) of a stationary black-hole. Second, the model possesses a mass gap. We show that the Eight-vertex Baxter model satisfies both the requirements. In the continuum limit, the Eight-vertex Baxter model is a massive free Fermion theory that is integrable with an infinite number of conserved charges. We show that this microscopic model explains the origin of the macroscopic properties of the horizon-fluid like bulk viscosity. Finally, we connect this model with Damours analysis and determine the mass-gap in the microscopic model.
According to the third law of Thermodynamics, it takes an infinite number of steps for any object, including black-holes, to reach zero temperature. For any physical system, the process of cooling to absolute zero corresponds to erasing information o
r generating pure states. In contrast with the ordinary matter, the black-hole temperature can be lowered only by adding matter-energy into it. However, it is impossible to remove the statistical fluctuations of the infalling matter-energy. The fluctuations lead to the fact the black-holes have a finite lower temperature and, hence, an upper bound on the horizon radius. We make an estimate of the upper bound for the horizon radius which is curiosly comparable to Hubble horizon. We compare this bound with known results and discuss its implications.
General Relativity predicts the existence of black-holes. Access to the complete space-time manifold is required to describe the black-hole. This feature necessitates that black-hole dynamics is specified by future or teleological boundary condition.
Here we demonstrate that the statistical mechanical description of black-holes, the raison detre behind the existence of black-hole thermodynamics, requires teleological boundary condition. Within the fluid-gravity paradigm --- Einsteins equations when projected on space-time horizons resemble Navier-Stokes equation of a fluid --- we show that the specific heat and the coefficient of bulk viscosity of the horizon-fluid are negative only if the teleological boundary condition is taken into account. We argue that in a quantum theory of gravity, the future boundary condition plays a crucial role. We briefly discuss the possible implications of this at late stages of black-hole evaporation.
Black-holes in asymptotically flat space-times have negative specific heat --- they get hotter as they loose energy. A clear statistical mechanical understanding of this has remained a challenge. In this work, we address this issue using fluid-gravit
y correspondence which aims to associate fluid degrees of freedom to the horizon. Using linear response theory and the teleological nature of event horizon, we show explicitly that the fluctuations of the horizon-fluid lead to negative specific heat for Schwarzschild black Hole. We also point out how the specific heat can be positive for Kerr-Newman or AdS black holes. Our approach constitutes an important advance as it allows us to apply canonical ensemble approach to study thermodynamics of asymptotically flat black-hole space-times.
For many years researchers have tried to glean hints about quantum gravity from black hole thermodynamics. However, black hole thermodynamics suffers from the problem of Universality --- at leading order, several approaches with different microscopic
degrees of freedom lead to Bekenstein-Hawking entropy. We attempt to bypass this issue by using a minimal statistical mechanical model for the horizon fluid based on Damour-Navier-Stokes (DNS) equation. For stationary asymptotically flat black hole spacetimes in General Relativity, we show explicitly that at equilibrium the entropy of the horizon fluid is the Bekenstein-Hawking entropy. Further we show that, for the bulk viscosity of the fluctuations of the horizon fluid to be identical to Damour, a confinement scale exists for these fluctuations, implying quantization of the horizon area. The implications and possible mechanisms from the fluid point of view are discussed.
In this work we study the statistical and thermodynamic properties of the horizon fluid corresponding to the Boulware-Deser (BD) black hole of Einstein-Gauss-Bonnet (EGB) gravity. Using mean field theory, we show explicitly that the BD fluid exhibits
the coexistence of two phases, a BEC and a non-condensed phase corresponding to the Einstein term and the Gauss-Bonnet term in the gravity action, respectively. In the fluid description, the high-energy corrections associated to Gauss-Bonnet gravity are modeled as excitations of the fluid medium. We provide statistical modeling of the excited part of the fluid and explicitly show that it is characterized by a generalized dispersion relation which in $D=6$ dimensions corresponds to a non-relativistic fluid. We also shed light on the ambiguity found in the literature regarding the expression of the entropy of the horizon fluid. We provide a general prescription to obtain the entropy and show that it is indeed given by Wald entropy.
Einstein equations projected on to a black hole horizon gives rise to Navier-Stokes equations. Horizon-fluids typically possess unusual features like negative bulk viscosity and it is not clear whether a statistical mechanical description exists for
such fluids. In this work, we provide an explicit derivation of the Bulk viscosity of the horizon-fluid based on the theory of fluctuations a la Kubo. The main advantage of our approach is that our analysis remains for the most part independent of the details of the underlying microscopic theory and hence the conclusions reached here are model independent. We show that the coefficient of bulk viscosity for the horizon-fluid matches exactly with the value found from the equations of motion for the horizon-fluid.
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.
For Rindler observers accelerating close to the horizon in local patches around a spacetime point, the matter-energy passing through the horizon increases the entropy and heat energy. Jacobson has showed that the Einstein equation can be derived from
the consideration of this thermodynamic process. This, however, works only if the acceleration $a$ is much larger than the scale set by the curvature of the spacetime. It is explored here whether an extension is possible to the case with no lower bound on $a$. We show that this is possible if one assumes that in a locally accelerating frame, the matter-energy passing through null hypersurfaces could result in an increase in the heat energy and the entropy. Such a generalisation extends the thermodynamic derivation of gravity to include any non-freely falling observer. A new method of determining the temperature detected by such locally accelerating observers is also presented. By considering only the quantisation of sufficiently localised wave modes of a field, it is shown that the observer finds himself in a thermal environment.
