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We develop a general algorithm that enables the consistent embedding of anyfour-dimensional static and spherically symmetric geometry into anyfive-dimensional single-brane braneworld model, characterized by an injectiveand nonsingular warp factor. Furthermore, we supplement the algorithm byintroducing a method that allows one to, in principle, reconstruct 5D fieldtheories that support the aforementioned geometries. This approach is based ona conformal transformation of the metric with the conformal factor beingidentified with the warp factor of the bulk geometry. The reconstructedtheories depend solely on the induced brane geometry, since the warp factor ismodel-independently represented by a scalar field in the Lagrangian density. Asa first application of our reconstruction method, we present for the first timea complete theory that supports the five-dimensional brane-localized extensionof the Schwarzschild black hole, for any warp factor. The same method issubsequently utilized to illustrate the process of coherently embedding a deSitter brane in braneworld models.

Bridging Dimensions: General Embedding Algorithm and Field-Theory Reconstruction in 5D Braneworld Models