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arXiv · 2505.06415

Are Pad\'e approximants suitable for modelling shape functions of traversable wormholes?

Jonathan Alves Rebouças·Celio Rodrigues Muniz
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Abstract

This study investigates the applicability of Pad\'e approximants in constructing suitable shape functions for traversable wormholes, emphasizing their ability to satisfy essential geometric constraints. By analyzing low-order Pad\'e approximants, we demonstrate their effectiveness in transforming inadequate shape functions into physically consistent candidates, while inherently fulfilling critical criteria such as asymptotic flatness, flare-out conditions, and throat regularity. Specific parameter restrictions are established to ensure compliance with these constraints; for instance, low-order rational approximations help to avoid artificial singularities and maintain asymptotic behavior when derivative conditions at the throat are controlled. In contrast, high-order Pad\'e approximants introduce challenges, including spurious poles within the physical domain, which disrupt geometric requirements. Our findings highlight that low-order Pad\'e approximants provide a robust framework for simplifying complex shape functions into analytically tractable forms, balancing mathematical flexibility with physical feasibility. This work underscores their potential as a systematic tool in traversable wormhole modeling, while cautioning against unphysical artifacts in higher-order approximations.

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Jonathan Alves Rebouças, Celio Rodrigues Muniz. 2025-05-09. Are Pad\'e approximants suitable for modelling shape functions of traversable wormholes?. https://doi.org/10.1016/j.aop.2025.170107

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