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Abstract
This paper develops a systematic framework for studying static, spherically symmetric perfect fluid configurations within the Einstein–Cartan– Sciama–Kibble (ECSK) theory of gravitation. The ECSK formalism extends classical general relativity by incorporating spacetime torsion as a geometrical field sourced by the intrinsic spin density of matter. We write down the governing field equations for the interior of a self-gravitating fluid sphere, exploit Hehl’s redefinition of effective thermodynamic variables to decouple the spin–torsion corrections, and derive a class of interior solutions by prescribing a barotropic equation of state together with a specific choice of one metric potential. The solutions are matched at the stellar surface to the Schwarzschild exterior via the Darmois–Israel junction conditions, yielding unique values for all integration constants. Explicit analytic expressions for the energy density, isotropic pressure, and spin density are presented and analysed. Physical viability is assessed through the standard energy conditions, regularity requirements, and monotonicity criteria. The investigation demonstrates that spin–torsion coupling introduces a repulsive pressure correction that can, under appropriate conditions, prevent the formation of central singularities and modify the mass–radius relationship of compact stellar objects. The astrophysical implications for neutron stars, quark stars, and other dense matter environments are discussed in detail.
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References
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