Abstract
This study presents novel solutions to the Einstein-Maxwell field equations by introducing an electromagnetic field into the generalized Tolman-Kuchowicz (GTK) metric framework, coupled with a van der Waals equation of state. The model is specifically applied to the ultra-massive pulsar PSR J0952-0607 under static, spherically symmetric, and anisotropic conditions. The incorporation of electric charge generates additional repulsive forces that counteract gravitational collapse, potentially enabling more compact and massive stellar configurations. PSR J0952-0607, with a mass of 2.35 ± 0.17M
⊙
, provides an excellent observational benchmark for examining the thermodynamic behavior of dense nuclear matter under electromagnetic influences. Through analytical solutions of the Einstein-Maxwell equations, we derive explicit expressions for energy density, radial and tangential pressures, electric field intensity, and the anisotropy factor. The model undergoes rigorous examination under the Tolman-Oppenheimer-Volkoff (TOV) equilibrium condition, now modified to incorporate charge, achieving precise balance among gravitational, hydrostatic, anisotropic, and electric forces. The resulting configurations satisfy all fundamental physical criteria, including causality conditions, energy conditions (NEC, WEC, DEC, SEC), appropriate adiabatic index bounds, and Herreras cracking stability criterion. All solutions exhibit regularity at the center and remain singularity-free throughout. A comprehensive graphical analysis demonstrates the model’s stability and parametric sensitivity across different values of the GTK parameter n = 1, 1.5, 2, 2.5 and charge parameter k. These findings contribute significantly to understanding the internal structure and stability mechanisms of ultra-massive charged compact stars within relativistic frameworks.