Abstract
General Relativity predicts the existence of black-holes. Access to the complete space-time manifold is required to describe black-holes. This strange 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, as required by the laws of black-hole thermodynamics, also requires teleological boundary condition. It is known for three decades that the Einstein's equations when projected on space-time horizons resemble Navier-Stokes equation of a fluid. Within this paradigm, 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 quantum theory of gravity, the future boundary condition plays a crucial role and discuss its implications.
SHANKARANARAYANAN S