Abstract

The authors provide a methodology for decoupling the bulk gravitational field equations of braneworld black holes (BHs) to suppress the bulk singularities. Thus, a regular braneworld BH setup is provided. To achieve this, a minimal geometric deformation is applied with respect to a coupling constant (Formula presented.) to the (Formula presented.) Minkowski spacetime embedded in an extra dimension. This results in a gravitational decoupling into a system (Formula presented.) with equations of motion of order (Formula presented.) and a system (Formula presented.), related to the so-called Quasi–Einstein equations of order (Formula presented.). This methodology allows for the construction of a regular geometry everywhere. The necessary constraints for eliminating singularities is outlined and provide a recipe for solving the equations of motion. Both the warp factor, the scalar field, and the potential obtained are smooth and free from Dirac delta singularities. A control parameter is introduced such that, in the limit (Formula presented.), the Randall–Sundrum setup is recovered, resulting in a transition from a thick brane to a thin brane. The asymptotic behavior of the curvature invariant (Formula presented.) is positive near the de Sitter core (for small (Formula presented.)), asymptotically negative for finite (Formula presented.), and asymptotically flat at the (Formula presented.) boundary as (Formula presented.). Although this work aims to suppress bulk singularities, it is expected that our methodology may be useful for future investigations related to the embedding of gravitational objects within other braneworld contexts. © 2025 Wiley-VCH GmbH.