General solution for the warp function in the RS scenario

TL;DR

This paper derives a comprehensive, symmetric solution for the warp function in the Randall-Sundrum model, addressing the geometry of the five-dimensional spacetime with branes and orbifold symmetry, expanding the understanding of possible configurations.

Contribution

It provides the most general symmetric solution for the warp function sigma(y) in the RS scenario, satisfying Einstein's equations and orbifold symmetry, with implications for diverse physical models.

Findings

Derived the general symmetric warp function sigma(y)

Reproduces derivative jumps at branes

Classifies physically diverse schemes

Abstract

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.