Static Spherically Symmetric Chaplygin and Polytropic Fluid Solutions in Teleparallel $F(T)$ Gravity

Abstract

We investigate static, spherically symmetric (SS) spacetimes in covariant teleparallel $F(T)$ gravity sourced by nonlinear Chaplygin and polytropic fluids. Using the covariant coframe/spin-connection (CSC) formalism, we derive the corresponding field equations and conservation laws governing admissible matter distributions and nonlinear torsion sectors. A general reconstruction procedure is developed, allowing the systematic determination of teleparallel $F(T)$ models for arbitrary coframe ansätze and fluid equations of state. Focusing on power-law configurations, we obtain several classes of reconstructed solution branches, including constant-radius, compact-object-like, and wormhole-like (WH-like) branches. The Chaplygin sector naturally leads to effective dark-energy-like and exotic-matter candidate solution branches within the reconstruction framework, which may provide admissible sectors for wormhole-like reconstructed geometries, while the polytropic sector provides reconstructed branches that may serve as physically motivated candidates for future stellar-interior and compact-object models. We discuss the associated candidate horizon and throat conditions, torsion singularities, energy conditions, and local viability properties of the reconstructed branches. The resulting geometries are organized within a teleparallel invariant classification framework, highlighting the role of nonlinear torsion corrections in shaping the solution space. Overall, this work provides a unified covariant reconstruction framework for nonlinear-fluid sectors in teleparallel $F(T)$ gravity, identifying solution branches that may serve as candidates for future compact-object, stellar-interior, and wormhole studies.

17 pages, 3 figures

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