  It has been known for several decades that Einstein's field equations, when
projected onto a null surface, exhibits a structure very similar to
non-relativistic Navier-Stokes equation. I show that this result arises quite
naturally when gravitational dynamics is viewed as an emergent phenomenon.
Extremising the spacetime entropy density associated with the null surfaces
leads to a set of equations which, when viewed in the local inertial frame,
becomes identical to the Navier-Stokes (NS) equation. This is in contrast with
the usual description of Damour-Navier-Stokes (DNS) equation in a general
coordinate system, in which there appears a Lie derivative rather than
convective derivative. I discuss this difference, its importance and why it is
more appropriate to view the equation in a local inertial frame. The viscous
force on fluid, arising from the gradient of the viscous stress-tensor,
involves the second derivatives of the metric and does not vanish in the local
inertial frame while the viscous stress-tensor itself vanishes so that inertial
observers detect no dissipation. We thus provide an entropy extremisation
principle that leads to the DNS equation, which makes the hydrodynamical
analogy with gravity completely natural and obvious. Several implications of
these results are discussed.
