paper

Are Padé approximants suitable for modelling shape functions of traversable wormholes?

arXiv:2505.06415 · doi:10.1016/j.aop.2025.170107

Abstract

This study investigates the applicability of Padé approximants in constructing suitable shape functions for traversable wormholes, emphasizing their ability to satisfy essential geometric constraints. By analyzing low-order Padé 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 Padé approximants introduce challenges, including spurious poles within the physical domain, which disrupt geometric requirements. Our findings highlight that low-order Padé 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.

References in corpus (17)