Generalization of the Randall–Sundrum solution

The generalization of the Randall–Sundrum solution for the warp factor exp⁡[σ(y)]exp⁡[σ(y)] in the scenario with one extra coordinate y  , non-factorizable space–time geometry and two branes is obtained. It is shown that the function obtained σ(y)σ(y) is symmetric with respect to an interchange of two branes. It also obeys the orbifold symmetry y→−yy→−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 result in theories with quite different spectra of the Kaluza–Klein gravitons.