  There are two different approaches to handle brane-world models brane-based
or bulk-based. In the brane-based approach, the brane is chosen to be fixed on
a coordinate system, whereas in the bulk-based approach, it is no longer static
as it moves along the extra dimension. It is aimed to get a general formalism
of the equivalence between two approaches obtained for a specific model in
Mukohyama et all [12]. We found that calculations driven by a general
anisotropic bulk-based metric yields a brane-based metric in Gaussian Normal
Coordinates by conserving spatial anisotropy.
