Generalization of the Randall-Sundrum solution

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.