A New Padé Approach to Modeling Wormholes in Dekel‐Zhao Dark Matter Halos

ABSTRACT We propose a new strategy for constructing traversable wormholes using Padé approximants, addressing the limitations of the standard ‘geometry‐first’ approach. We demonstrate that directly expanding the shape function can introduce spurious poles and fails to guarantee fidelity to the target matter distribution. To resolve these issues, we introduce a ‘matter‐first’ method, where the density profile is approximated by rational functions and then integrated to derive the shape function. This approach ensures that the resulting spacetime exactly reproduces the intended matter content while providing analytical closed‐form solutions, as Padé approximants are inherently integrable. We apply this framework to the Dekel–Zhao dark matter halo, showing that the matter‐first construction yields globally regular geometries that satisfy asymptotic flatness and flare‐out conditions without the artificial singularities found in the geometry‐first scheme. Finally, we analyze the energy conditions, confirming that the method provides a controlled and consistent description of the wormhole throat and its supporting exotic matter.