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

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 energymomentum 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.

Energy Definition and Dark Energy: A Thermodynamic Analysis

“…Although this energy definition has originally been obtained by using the Einstein field equations [47], it is in accordance with various thermodynamic and holographic approaches [34][35][36][37][38][39][40][41][42][43][44][45][46]. In fact, if we accept this energy definition as a basic equation and not a secondary equation [34][35][36][37], then there are various thermodynamic and holographic approaches employed to get the Friedmann and gravitational field equations in various theories by using the Komar mass definition [34][35][36][37][38][39][40][41][42][43][44][45][46]. Now, inserting the Komar energy definition into Eq.…”

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