The model treats the star’s matter as anisotropic, with pressure and energy density varying differently in radial and tangential directions, and uses a polytropic equation of state to relate pressure to energy density. Two parameters shape the predicted interior: the metric exponent in the generalized Tolman–Kuchowicz solution and the polytropic index. Their effects on the star were examined through three-dimensional plots combining radial profiles with comparisons across parameter values, including energy density, radial and tangential pressures, anisotropy, sound speeds, adiabatic indices and hydrostatic equilibrium.

Across the modeled configurations, the physical quantities were described as well behaved throughout the stellar interior. The analysis also checked the Tolman–Oppenheimer–Volkoff equation, a relativistic equation used to test the internal hydrostatic balance of compact stellar models. Causality, Herrera’s cracking criterion and the requirement that the adiabatic index exceed 4/3 were reported as satisfied. These results are consistency tests within the assumed model, not direct measurements of conditions inside the pulsar or proof that the star is stable against every possible perturbation.

The resulting mass and compactness profiles were found to be compatible with representative constraints derived from NICER observations of massive neutron stars. The authors therefore conclude that anisotropic polytropic configurations are physically viable descriptions of ultra-massive neutron stars such as PSR J0952–0607. The result does not uniquely determine the pulsar’s internal composition, and its dependence on the chosen equation of state, anisotropy prescription and model parameters limits how broadly it can be applied. Even so, it shows that a pulsar approaching three solar masses can satisfy several standard physical criteria when its interior is treated with a relativistic anisotropic framework.

Subject of Research: Relativistic modeling of the internal structure and physical viability of the massive pulsar PSR J0952–0607

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

Article References: Riaz, M. B., Zahra, A., & Mardan, S. A. (2026). Physical viability of the massive pulsar PSR J0952–0607 within a polytropic framework. PLOS One, 21(10), e0359628. https://doi.org/10.1371/journal.pone.0359628

Image Credits: AI Generated

DOI: 10.1371/journal.pone.0359628

Keywords: PSR J0952–0607, massive neutron stars, relativistic stellar structure, anisotropic matter, polytropic equation of state, Tolman–Oppenheimer–Volkoff equation, causality, stellar stability, NICER, Einstein field equations, Physical, viability