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Abstract <p>We present new exact solutions to the Einstein–Cartan (EC) field equations for static, spherically symmetric configurations of a noncharged Weyssenhoff fluid in isotropic coordinates, derived using the extended technique of differential forms applied to the non-Riemannian space-time of the Einstein–Cartan theory of gravitation (ECTG). The solutions exhibit regular behavior with nonnegative pressure and energy density, and satisfy the adiabatic stability condition <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({1/\sqrt{3}&lt;a&lt;1}\)</EquationSource> <!--GravCos2570033Katkar-m1--> </InlineEquation>. All models are rotating and accelerating, with vanishing expansion and shear. Spin contributions explicitly influence the matter distribution; in the spinless limit, the solutions reduce to those of Narlikar and Kuchowicz. For specific parameter values <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(n\)</EquationSource> <!--GravCos2570033Katkar-m2--> </InlineEquation>&#xa0;(<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\sqrt{2}\leq n\leq 2\)</EquationSource> <!--GravCos2570033Katkar-m3--> </InlineEquation>), the models may be applicable to neutrino geodesic motion and other compact object studies in EC gravity.</p>

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Isotropic Spherically Symmetric Weyssenhoff Fluid Sphere Models in Einstein–Cartan Theory

  • 期刊论文

  • 发表日期：

    2025年12月3日

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  • L. N. Katkar,
  • D. R. Phadatare

摘要

Abstract

We present new exact solutions to the Einstein–Cartan (EC) field equations for static, spherically symmetric configurations of a noncharged Weyssenhoff fluid in isotropic coordinates, derived using the extended technique of differential forms applied to the non-Riemannian space-time of the Einstein–Cartan theory of gravitation (ECTG). The solutions exhibit regular behavior with nonnegative pressure and energy density, and satisfy the adiabatic stability condition \({1/\sqrt{3}<a<1}\) . All models are rotating and accelerating, with vanishing expansion and shear. Spin contributions explicitly influence the matter distribution; in the spinless limit, the solutions reduce to those of Narlikar and Kuchowicz. For specific parameter values \(n\)  ( \(\sqrt{2}\leq n\leq 2\) ), the models may be applicable to neutrino geodesic motion and other compact object studies in EC gravity.