Phase structure of Power–Yang–Mills black holes in a Scalar Murnaghan EoS Medium

In this paper, we present a new static, spherically symmetric black hole solution in an asymptotically anti-de Sitter spacetime, derived from a Power–Yang–Mills (PYM) sector and a Murnaghan matter sector, and analyze its thermodynamic and geometric properties both analytically and numerically. In the normal phase space, we compute the Hawking temperature and identify the physical limits on positive temperatures. The extended phase space analysis includes heat capacity, criticality studies, and thermodynamic geometry using the Hendi–Panahiyan–Eslam Panah–Momennia (HPEM) Ricci scalar. The equation of state and Gibbs free energy facilitates the derivation of criticality conditions. We demonstrate that the PYM term influences small-horizon behavior while the Murnaghan sector affects intermediate-range corrections and energy-condition violations. The analytic collapse criterion based on Murnaghan derivatives allows for testing stability between the PYM term and Murnaghan terms. Numerically, we derive critical triplets, verify mean-field critical exponents, and observe the interaction of PYM strength and Murnaghan amplitudes on phase transitions in this composite matter black hole family.

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