Entropy density of spacetime and the Navier-Stokes fluid dynamics of null surfaces
- Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune, Maharashtra 411 007 (India)
It has been known for several decades that Einstein's field equations, when projected onto a null surface, exhibit a structure very similar to the nonrelativistic Navier-Stokes equation. I show that this result arises quite naturally when gravitational dynamics is viewed as an emergent phenomenon. Extremizing 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 equation. This is in contrast to the usual description of the Damour-Navier-Stokes equation in a general coordinate system, in which there appears a Lie derivative rather than a 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 extremization principle that leads to the Damour-Navier-Stokes equation, which makes the hydrodynamical analogy with gravity completely natural and obvious. Several implications of these results are discussed.
- OSTI ID:
- 21505006
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 83, Issue 4; Other Information: DOI: 10.1103/PhysRevD.83.044048; (c) 2011 American Institute of Physics; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
DENSITY
EINSTEIN FIELD EQUATIONS
ENTROPY
FLUID MECHANICS
GRAVITATION
METRICS
NAVIER-STOKES EQUATIONS
SPACE-TIME
SURFACES
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD EQUATIONS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
THERMODYNAMIC PROPERTIES