Field Equations for Lovelock Gravity: An Alternative Route

Sumanta Chakraborty (Department of Theoretical Physics, Indian Association for the Cultivation of Science, Kolkata 700032, India)

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.

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      "value": "We present an alternative derivation of the gravitational field equations for Lovelock gravity starting from Newton\u2019s 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\u2019s equation, Einstein\u2019s 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."
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Published on:
19 April 2018
Publisher:
Hindawi
Published in:
Advances in High Energy Physics (2018)

DOI:
https://doi.org/10.1155/2018/6509045
arXiv:
1704.07366v1
Copyrights:
Copyright © 2018 Sumanta Chakraborty.
Licence:
CC-BY-3.0

Fulltext files: