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arXiv · 1607.06844

From the Komar Mass and Entropic Force Scenarios to the Einstein Field Equations on the Ads Brane

H. Moradpour·A. Sheykhi
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Abstract

By bearing the Komar's definition for the mass, together with the entropic origin of gravity in mind, we find the Einstein field equations in $(n+1$)-dimensional spacetime. Then, by reflecting the ($4+1$)-dimensional Einstein equations on the ($3+1$)-hypersurface, we get the Einstein equations onto the $3$-brane. The corresponding energy conditions are also addressed. Since the higher dimensional considerations modify the Einstein field equations in the ($3+1$)-dimensions and thus the energy-momentum tensor, we get a relation for the Komar mass on the brane. In addition, the strongness of this relation compared with existing definition for the Komar mass on the brane is addressed.

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H. Moradpour, A. Sheykhi. 2016-05-14. From the Komar Mass and Entropic Force Scenarios to the Einstein Field Equations on the Ads Brane. https://doi.org/10.1007/s10773-015-2756-2

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