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

TL;DR

This paper derives Einstein field equations on a 3-brane from higher-dimensional theories using Komar mass and entropic gravity concepts, analyzing modifications to energy conditions and mass definitions.

Contribution

It presents a novel derivation of Einstein equations on a brane from higher-dimensional spacetime using entropic and Komar mass principles.

Findings

Einstein equations on the brane are derived from higher-dimensional spacetime.

Modified energy conditions are discussed in the brane context.

A new relation for Komar mass on the brane is proposed.

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.