Structure of the gravitational action and its relation with horizon thermodynamics and emergent gravity paradigm

Parattu, Krishnamohan ; Majhi, Bibhas Ranjan ; Padmanabhan, T. (2013) Structure of the gravitational action and its relation with horizon thermodynamics and emergent gravity paradigm Physical Review D - Particles, Fields, Gravitation and Cosmology, 87 (12). Article ID 124011, 24 pages. ISSN 1550-7998

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Official URL: http://prd.aps.org/abstract/PRD/v87/i12/e124011

Related URL: http://dx.doi.org/10.1103/PhysRevD.87.124011

Abstract

If gravity is an emergent phenomenon, as suggested by several recent results, then the structure of the action principle for gravity should encode this fact. With this motivation we study several features of the Einstein-Hilbert action and establish direct connections with horizon thermodynamics. We begin by introducing the concept of holographically conjugate variables in terms of which the surface term in the action has a specific relationship with the bulk term. In addition to gab and its conjugate momentum √−gMcab, this procedure allows us to (re)discover and motivate strongly the use of fab=−g√-ggab and its conjugate momentum Ncab. The gravitational action can then be interpreted as a momentum-space action for these variables. We also show that many expressions in classical gravity simplify considerably in this approach. For example, the field equations can be written in the form ∂cfab=∂Hg/∂Ncab, ∂cNcab=−∂Hg/∂fab (analogous to Hamilton’s equations) for a suitable Hamiltonian Hg, if we use these variables. More importantly, the variation of the surface term, evaluated on any null surface which acts a local Rindler horizon can be given a direct thermodynamic interpretation. The term involving the variation of the dynamical variable leads to TδS while the term involving the variation of the conjugate momentum leads to SδT. We have found this correspondence only for the choice of variables (gab,√-gMcab) or (fab,Ncab). We use this result to provide a direct thermodynamical interpretation of the boundary condition in the action principle, when it is formulated in a spacetime region bounded by the null surfaces. We analyze these features from several different perspectives and provide a detailed description, which offers insights about the nature of classical gravity and emergent paradigm.

Item Type:Article
Source:Copyright of this article belongs to The American Physical Society.
ID Code:97931
Deposited On:16 Jan 2014 10:37
Last Modified:22 Jan 2014 09:04

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