Warp Factors and Extended Sources in Two Transverse Dimensions

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.