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Abstract
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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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