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±0.17M⊙ and radius 13.7-1.5+2.6 km 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.