Non-Compact Matter Sources and Their Role in Black Hole Thermodynamics: A Mathematical Study

Source abstract

In this study, we examine the thermodynamic behavior of a charged black hole arising from a non-compact matter source under the influence of a non-commutative parameter. We analyze key thermodynamic quantities including the event horizon, Hawking temperature, and heat capacity. The inversion temperature and associated inversion curves are derived, revealing the conditions under which phase transitions occur. A comparative study between charged and uncharged black holes is conducted, highlighting both similarities and differences in their thermodynamic behavior.Our analysis of the Ricci scalar and related curvature invariants shows that while these quantities exhibit singular behavior at the origin, the non-singular nature of the proposed metric leads to a space-like singularity. The transition from a two-horizon black hole to an extremal black hole with a degenerate horizon is investigated in the framework of Hawking temperature analysis.Graphical analyses are presented for various values of charge, revealing a nonlinear relationship between pressure and temperature. Furthermore, the equation of state is studied for both Schwarzschild and Reissner-Nordström black holes under the influence of the non-commutative parameter. These results provide deeper insight into the thermodynamics of black holes in modified gravity scenarios.