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

TL;DR

This paper evaluates the use of low-order Padé approximants for modeling shape functions in traversable wormholes, demonstrating their effectiveness in satisfying geometric constraints and highlighting limitations of higher-order approximations.

Contribution

It introduces a systematic approach using low-order Padé approximants to generate physically consistent wormhole shape functions, addressing issues of singularities and asymptotic behavior.

Findings

Low-order Padé approximants effectively satisfy geometric constraints.

High-order approximants can introduce spurious poles and artifacts.

Parameter restrictions ensure physical and mathematical consistency.

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.