A Brane World in an Arbitrary Number of Dimensions without Z_2 Symmetry

Understand

We consider a brane world in an arbitrary number of dimensions without Z_2 symmetry and derive the effective Einstein equation on the brane, where its right-hand side is given by the matter on the brane and the curvature in the bulk.

• This is achieved by first deriving the junction conditions for a non-Z_2 symmetric brane and second solving the Gauss equation, which relates the mean extrinsic curvature of the brane to the curvature in the bulk, with respect to the mean extrinsic curvature.
• The latter corresponds to formulating an explicit junction condition on the mean of the extrinsic curvature, analogue to the Israel junction condition for the jump of the extrinsic curvature.
• We find that there appears a new type of an effective anisotropic fluid on the right-hand side of the effective Einstein equation due to the fact that there is no Z_2 symmetry.