Field Equations for Lovelock Gravity: An Alternative Route

We present an alternative derivation of the gravitational field equations for Lovelock gravity starting from Newton’s law, which is closer in spirit to the thermodynamic description of gravity. As a warm up exercise, we have explicitly demonstrated that, projecting the Riemann curvature tensor appro...

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Bibliographic Details
Main Author: Sumanta Chakraborty
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Advances in High Energy Physics
Online Access:http://dx.doi.org/10.1155/2018/6509045
Description
Summary:We present an alternative derivation of the gravitational field equations for Lovelock gravity starting from Newton’s law, which is closer in spirit to the thermodynamic description of gravity. As a warm up exercise, we have explicitly demonstrated that, projecting the Riemann curvature tensor appropriately and taking a cue from Poisson’s equation, Einstein’s equations immediately follow. The above derivation naturally generalizes to Lovelock gravity theories where an appropriate curvature tensor satisfying the symmetries as well as the Bianchi derivative properties of the Riemann tensor has to be used. Interestingly, in the above derivation, the thermodynamic route to gravitational field equations, suited for null hypersurfaces, emerges quiet naturally.
ISSN:1687-7357
1687-7365