Warped Geometry in Higher Dimensions with an Orbifold Extra Dimension

We solve the Einstein equations in higher dimensions with warped geometry where an extra dimension is assumed to have orbifold symmetry, S/Z2. The setup considered here is an extension of the 5-dimensional Randall-Sundrum model to (5+D)-dimensions, and hidden and observable branes are fixed on the orbifold. It is assumed that the brane tension (self-energy) of each brane with (4+D)-dimensional spacetime is anisotropic and that the warped metric function of the 4-dimensions is generally different from the one of the extra D-dimensions. We point out that the form of the warped metric functions and the relations between tensions of two branes depend on the integration constant appearing in the Einstein equations as well as the sign of the bulk cosmological constant. E-mail address: [email protected]