General solution for the warp function in the RS scenario

The five-dimensional space-time, with non-factorizable geometry and fifth dimension y being an orbifold S^1/Z_2, is studied. In such a scenario, originally suggested by Randall and Sundrum, there exist two branes at fixed points of the orbifold, and the four-dimensional metric is multiplied by a warp factor exp[sigma(y)]. In the present paper, the general solution sigma(y) of the Einstein-Hilbert's equations is presented which is symmetric with respect to the interchange of two branes. It obeys the orbifold symmetry y -> - y and explicitly reproduces jumps of its derivative on both branes. This general solution for sigma(y) is determined by the Einstein-Hilbert's equations up to a constant, that results in physically diverse schemes.

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