Energy-momentum for Randall-Sundrum models

TL;DR

This paper studies the energy-momentum conservation in Randall-Sundrum models, revealing that energy is localized near the Planck brane with a specific exponential decay, and the momentum vanishes.

Contribution

It provides a detailed analysis of energy-momentum conservation laws in Randall-Sundrum models using the displacement transform, highlighting energy localization and momentum behavior.

Findings

Energy is localized near the Planck brane with exponential decay.

Momentum vanishes in the Randall-Sundrum solution.

Energy density follows an exponential profile $oxed{ ext{ } ext{ extbackslash} ext{ extbar} y ext{ extbackslash} ext{ extbar} ext{ extbackslash} ext{ extbackslash} 3k ext{ extbackslash} ext{ extbar} y ext{ extbackslash} ext{ extbackslash} 0}$.

Abstract

We investigate the conservation law of energy-momentum for Randall-Sundrum models by the general displacement transform. The energy-momentum current has a superpotential and are therefore identically conserved. It is shown that for Randall-Sundrum solution, the momentum vanishes and most of the bulk energy is localized near the Planck brane. The energy density is $\epsilon = \epsilon_0 e^{-3k \mid y \mid}$.