Generalization of the Randall-Sundrum solution

TL;DR

This paper generalizes the Randall-Sundrum solution for warped extra dimensions, showing how the warp factor can be symmetrically extended with different spectra of Kaluza-Klein gravitons based on a constant parameter.

Contribution

It provides a new, symmetric form of the warp factor in a two-brane scenario, expanding the understanding of extra-dimensional models and their graviton spectra.

Findings

Warp factor sigma(y) is symmetric under brane interchange.

The solution obeys orbifold symmetry y -> - y.

Different constant C values lead to varied Kaluza-Klein graviton spectra.

Abstract

The generalization of the Randall-Sundrum solution for the warp factor exp[sigma(y)] in the scenario with one extra coordinate y, non-factorizable space-time geometry and two branes isobtained. It is shown that the function obtained sigma(y) is symmetric with respect to an interchange of two branes. It also obeys the orbifold symmetry y -> - y and explicitly reproduces jumps of its derivative on both branes. This solution is defined by the Einstein-Hilbert's equations up to a constant C. It is demonstrated that different values of C results in theories with quite different spectra of the Kaluza-Klein gravitons.