Brane World of Warp Geometry: An Introductory Review

TL;DR

This paper provides an introductory review of the Randall-Sundrum brane world models, detailing their metrics, implications for the hierarchy problem, and derivation of Newtonian gravity from small fluctuations.

Contribution

It offers a detailed, step-by-step derivation and explanation of the Randall-Sundrum models, clarifying their geometric structure and physical implications.

Findings

Randall-Sundrum Model I alleviates the gauge hierarchy problem.

Model II reproduces Newtonian gravity from brane fluctuations.

Explicit metrics for both models are constructed and analyzed.

Abstract

Basic idea of Randall-Sundrum brane world model I and II is reviewed with detailed calculation. After introducing the brane world metric with exponential warp factor, metrics of Randall-Sundrum models are constructed. We explain how Randall-Sundrum model I with two branes makes the gauge hierarchy problem much milder, and then derive Newtonian gravity in Randall-Sundrum model II with a single brane by considering small fluctuations.