It has recently been proposed that the hierarchy problem can be solved by considering the warped fifth dimension compactified on S^1/Z_2. Many studies in the context have assumed a particular choice for an integration constant σ_0 that appears when one solves the five-dimensional Einstein equation. Since σ_0 is not determined by the boundary condition of the five-dimensional theory, σ_0 may be regarded as a gauge degree of freedom in a sense. To this time, all indications are that the

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... sional Planck mass depends on σ_0. In this paper, we carefully investigate the properties of the geometry in the Randall-Sundrum model, and consider in which location y the four-dimensional Planck mass is measured. As a result, we find a σ_0-independent relation between the four-dimensional Planck mass M_ Pl and five- dimensional fundamental mass scale M, and remarkably enough, we can take M to TeV region when we consider models with the Standard Model confined on a distant brane. We also confirm that the physical masses on the distant brane do not depend on σ_0 by considering a bulk scalar field as an illustrative example. The resulting mass scale of the Kaluza-Klein modes is on the order of M.