Physical viability of the massive pulsar PSR J0952–0607 within a polytropic framework

We develop a relativistic model for one of the most massive pulsars, PSR J0952-0607, by constructing exact solutions of Einstein’s field equations (EFEs) within the framework of the generalized Tolman–Kuchowicz (GTK) spacetime. The stellar interior is modeled as anisotropic matter governed by a polytropic equation of state (EoS). This framework allows for a systematic investigation of how the GTK metric exponent m and the polytropic index n influence the internal structure and stability of the star. The physical characteristics of the model are analyzed using three-dimensional graphical representations. These plots simultaneously display the dependence of key variables on the radial coordinate as well as on the model parameters m and n . By smoothly matching the interior solution to the exterior Schwarzschild spacetime, the model parameters are constrained using the measured mass M = 2.35 ± 0.17 M ⊙ and radius 13.7 − 1.5 + 2.6 k m estimates of PSR J0952-0607. We analyze the radial behavior of the energy density, radial and tangential pressures, anisotropy, sound speeds, adiabatic indices, and hydrostatic equilibrium through the Tolman–Oppenheimer–Volkoff (TOV) equation. All physical quantities remain finite, positive and well behaved, while the causality condition, Herrera’s cracking criterion, and the relativistic stability requirement Γ > 4 / 3 are satisfied throughout the stellar interior. The model fulfills all standard energy conditions and yields mass and compactness profiles compatible with representative NICER-based constraints for massive neutron stars. This shows the physical viability of anisotropic polytropic configurations for ultra-massive neutron stars.