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We consider a QCD cold plasma motivated Equation of State (EOS) to examinethe impact of an Anomalous Magnetic Moment (AMM) coupling and small shapedeformations for static oblate and prolate core shapes of quark stars. Usingthe Foga\c{c}a QCD motivated EOS which shifts from the high temperature lowchemical potential quark gluon plasma environment to the low temperature highchemical potential quark stellar core environment we consider the impact of anAMM coupling with a metric induced shape deformation parameter in the TOVequations. The EOS is developed using a hard gluon and soft gluon decompositionof the gluon field tensor using a mean field effective mass for the gluons. TheAMM is considered using the Dirac spin tensor coupled to the EM field tensorwith quark flavor based magnetic moments. The shape parameter is introduced ina metric ansatz that represents oblate and prolate static stellar cores formodified TOV equations. These equations are numerically solved for the finalmass and radius states representing the core collapse of a massive star with aphase transition leading to an unbound quark-gluon plasma. We find that thecombined shape parameter and AMM effects can alter the coupled EOS-TOVequations resulting in an increase in the final mass and a decrease in thefinal equatorial radius without collapsing the core into a black hole andwithout violating causality constraints, we find maximum mass values in therange: 2.3 Solar Masses < M < 2.7 Solar Masses. These states are consistentwith some astrophysical high mass magnetar/pulsar and gravity wave systemswhich may provide evidence for a core that has undergone a quark-gluon phasetransition such as PSR 0943+10 and the secondary from the GW 190814 event.

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