Warped Geometry in Higher Dimensions with an Orbifold Extra Dimension

TL;DR

This paper extends the Randall-Sundrum model to higher dimensions with an orbifold extra dimension, solving Einstein's equations for warped geometries with anisotropic brane tensions and analyzing the resulting metric functions.

Contribution

It provides solutions to Einstein's equations in higher-dimensional warped geometries with orbifold symmetry, considering anisotropic brane tensions and their effects on the metric.

Findings

Warped metric functions depend on integration constants and bulk cosmological constant.

Relations between brane tensions and metric functions are derived.

The model generalizes the Randall-Sundrum setup to higher dimensions.

Abstract

We solve the Einstein equations in higher dimensions with warped geometry where an extra dimension is assumed to have orbifold symmetry $S^{1}/Z_{2}$. The setup considered here is an extension of the five-dimensional Randall-Sundrum model to $5+D$ dimensions, and hidden and observable branes are fixed on the orbifold. It is assumed that the brane tension (self-energy) of each brane with $(4+D)$-dimensional spacetime is anisotropic and that the warped metric function of the four dimensions is generally different from that of the extra $D$ dimensions. We point out that the forms of the warped metric functions and the relations between the tensions of two branes depend on the integration constant appearing in the Einstein equations as well as on the sign of the bulk cosmological constant.