Warp Factors and Extended Sources in Two Transverse Dimensions

TL;DR

This paper explores solutions to Einstein's equations for parallel branes in a space with two curved transverse dimensions, highlighting the role of warp factors in higher-dimensional gravity and their implications for large extra dimensions.

Contribution

It generalizes known (2+1)-dimensional gravity solutions to higher dimensions with curved transverse spaces, providing a simple algebraic method to determine the metric and warp factors.

Findings

Solutions are characterized by roots of a simple algebraic equation.

Warp factors are explicitly determined at brane positions.

The results have implications for models with large extra dimensions.

Abstract

We study the solutions of the Einstein equations in (d+2)-dimensions, describing parallel p-branes (p=d-1) in a space with two transverse dimensions of positive gaussian curvature. These solutions generalize the solutions of Deser and Jackiw of point particle sources in (2+1)-dimensional gravity with cosmological constant. Determination of the metric is reduced to finding the roots of a simple algebraic equation. These roots also determine the nontrivial "warp factors" of the metric at the positions of the branes. We discuss the possible role of these solutions and the importance of "warp factors" in the context of the large extra dimensions scenario.