Action principle for the fluid-gravity correspondence and emergent gravity

Kolekar, Sanved ; Padmanabhan, T. (2012) Action principle for the fluid-gravity correspondence and emergent gravity Physical Review D, 85 (2). 024004. ISSN 1550-7998

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Official URL: http://prd.aps.org/abstract/PRD/v85/i2/e024004

Related URL: http://dx.doi.org/10.1103/PhysRevD.85.024004

Abstract

It has been known for a long time that Einstein’s field equations when projected onto a black hole horizon look very similar to a Navier-Stokes equation in suitable variables. More recently, it was shown that the projection of Einstein’s equation onto any null surface in any spacetime reduces exactly to the Navier-Stokes form when viewed in the freely falling frame. We develop an action principle, the extremization of which leads to the above result, in an arbitrary spacetime. The degrees of freedom varied in the action principle are the null vectors in the spacetime and not the metric tensor. The same action principle was introduced earlier in the context of the emergent gravity paradigm wherein it was shown that the corresponding Lagrangian can be interpreted as the entropy density of spacetime. The current analysis strengthens this interpretation and reinforces the idea that field equations in gravity can be thought of as emergent. We also find that the degrees of freedom on the null surface are equivalent to a fluid with equation of state PA=TS. We demonstrate that the same relation arises in the context of a spherical shell collapsing to form a horizon.

Item Type:Article
Source:Copyright of this article belongs to American Physical Society.
ID Code:96231
Deposited On:17 Dec 2012 09:21
Last Modified:19 May 2016 08:45

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