Non-static spinning fluid model in Einstein–Cartan theory of gravitation

Abstract By harnessing the power of differential forms, especially suited for a non-Riemannian space-time of Einstein–Cartan theory, we have successfully solved the field equations for a Weyssenhoff fluid-a fascinating source of gravitation and spin. Our innovative approach is based on a simple yet elegant equation of state, with two distinct cases: (i) $$\rho $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ρ</mml:mi> </mml:math> = p , and (ii) $$\rho = 3p$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ρ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mi>p</mml:mi> </mml:mrow> </mml:math> , and an exponential relationship $$e^{\mu } = e^{n\nu }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mi>μ</mml:mi> </mml:msup> <mml:mo>=</mml:mo> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:mi>n</mml:mi> <mml:mi>ν</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . We explore the fascinating physical and geometrical properties of these ground-breaking solutions, uncovering new insights into the mysteries of gravitation and the behavior of matter under extreme conditions.