Nonmetricity-based hybrid self-gravitating compact stars with embedded class-one symmetry

Abstract This work aims to explore the novel characteristics of a static hybrid transitional star with a spherical distribution of relativistic matter under the embedded class one metric framework. This theoretical stellar model is derived using the nonmetricity-inspired $$f(\mathbb {Q})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> gravity, featuring a core-crust structure: a strange matter core embedded in a normal matter crust. Our model incorporates pressure anisotropy as an intrinsic characteristic of highly compact strange stars, a feature expected to arise in the super-dense regime. The equation of state, in its basic form, using the MIT bag model is employed to represent correlation between pressure and density in quark matter inside the star’s core. The development of this model involves selecting the temporal gravitational potential based on the Tolman–Kuchowicz ansatz, while the radial gravitational potential is determined using the Class One embedding formalism. We employed both analytical and graphical methods to assess the robustness and equilibrium of the presented stellar solution. We provide an in-depth description of the astrophysical features of the model and show that they fulfill regularity requirements. A key finding of this investigation is the absence of a core singularity within the anisotropic stellar formation. The solution matches the properties of the observed self-gravitating pulsar objects: SAX J1804.4-3658 (SS1), EXO1745-248, 4U1820-30, 4U1608-52, PSR J0740+6620, PSR J0030+0451, Cen X-4, and SAX J1804.4-3658 (SS2).