Stable configurations of PSR J0952-0607 by using anisotropic generalized Tolman–Kuchowicz spacetime

Abstract In this work, we present solutions to Einstein’s field equations using a generalized Tolman–Kuchowicz metric with van der Waals equation of state. The model is applied on compact star PSR J0952-0607 in a static, spherically symmetric and anisotropic regime. The selected pulsar PSR J0952-0607 is known as the most massive neutron star to date, which captures the thermodynamic behavior of dense stellar matter more realistically. To ensure physical viability, the model is examined under the Tolman–Oppenheimer–Volkoff equilibrium condition, balancing internal pressure against gravitational pull. The resulting configurations satisfy essential physical conditions, including causality, energy conditions, appropriate adiabatic index bounds, and Herrera’s cracking criterion. The presented solutions remain regular at the center and are free from singularities. A detailed graphical analysis demonstrates the model’s stability and sensitivity across different values of the generalized Tolman–Kuchowicz parametric values $$n=1,1.5,2,2.5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1.5</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2.5</mml:mn> </mml:mrow> </mml:math> . These results offer valuable insights into the internal structure and stability of ultra-massive compact stars in modified relativistic frameworks.