Cold Quark–Gluon Plasma EOS Applied to a Magnetically Deformed Quark Star with an Anomalous Magnetic Moment

We consider a QCD cold-plasma-motivated Equation of State (EOS) to examine the impact of an Anomalous Magnetic Moment (AMM) coupling and small shape deformations on the static oblate and prolate core shapes of quark stars. Using the Fogaça QCD-motivated EOS, which shifts from the high-temperature, low-chemical-potential quark–gluon plasma environment to the low-temperature, high-chemical-potential quark stellar core environment, we consider the impact of an AMM coupling with a metric-induced shape deformation parameter in the Tolman–Oppenheimer–Volkov (TOV) equations. The AMM coupling includes a phenomenological scaling that accounts for the weak and strong field characteristics in dense matter. The EOS is developed using a hard gluon and soft gluon decomposition of the gluon field tensor and using a mean-field effective mass for the gluons. The AMM is considered using the Dirac spin tensor coupled to the EM field tensor with quark-flavor-based magnetic moments. The shape parameter is introduced in a metric ansatz that represents oblate and prolate static stellar cores for modified TOV equations. These equations are numerically solved for the final mass and radius states, representing the core collapse of a massive star with a phase transition leading to an unbound quark–gluon plasma. We find that the combined shape parameter and AMM effects can alter the coupled EOS–TOV equations, resulting in an increase in the final mass and a decrease in the final equatorial radius without collapsing the core into a black hole and without violating causality constraints; we find maximum mass values in the range 1.6 Mʘ < M < 2.5 Mʘ. These states are consistent with some astrophysical, high-mass magnetar/pulsar and gravity wave systems and may provide evidence for a core that has undergone a quark–gluon phase transition such as PSR 0943 + 10 and the secondary from the GW 190814 event.