Hydrodynamics of the atoms of spacetime: Gravitational field equation is navier-stokes equation

Abstract

There is consider able evidence to suggest that field equations of gravity have the same conceptual status as the equations of hydrodynamics or elasticity. We add further sup-port to this paradigm by showing that Einsteins field equations are identical in form to Navier –Stokes equations of hydrodynamics , when projected on to any null surface. In fact, these equations can be obtained directly by extremizing of entropy associated with the deformations of null surfaces thereby providing a completely thermodynamic route to gravitational field equations . Several curious features of this remarkable connection (including a phenomenon of dissipation without dissipation) are described and the implications for the emergent paradigm of gravity is highlighted.