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Bekenstein-Hawking entropy from Criticality

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.