Impacts of {$f(R, T)$} gravity on neutron stars study within the relativistic mean-field model framework in light of GW170817, Pulsars and NICER data

Abstract

In this work, we investigate the neutron star structure in conservative $f(R, T)$ gravity with $f(R, T)=R+\lambda T$, where $\lambda$ denotes the matter--geometry coupling. The modified stellar structure equations are solved using realistic relativistic mean-field (RMF) equations of state (EOSs), including density-dependent linear models and nonlinear interacting models with meson self-couplings. Theoretical predictions are confronted with multimessenger constraints from heavy pulsars, NICER radius measurements, and GW170817 tidal deformability, imposing $M_{\max}\simeq 2.07\, M_{\odot}$ and $10.62~\mathrm{km}<R_{1.4}<12.83~\mathrm{km}$ to constrain both the EOS parameter space and $\lambda$. We find that density-dependent EOSs such as DDH$_\delta$ and TW satisfy all observational constraints for specific $\lambda$ ranges, while nonlinear EOSs (NL3, GM1, TM1), despite large maximum masses, fail to simultaneously satisfy radius and tidal bounds even in modified gravity. The maximum neutron star mass is highly sensitive to the matter--geometry coupling and exhibits a strong degeneracy with the EOS, consistent with previous studies. The additional term in the modified Tolman--Oppenheimer--Volkoff equations alters the pressure gradient, affecting EOS stiffness and the speed of sound squared $c_s^2$, while preserving causality ($c_s^2/c^2<1$). Pearson and Kendall analyses reveal a strong negative correlation between mass, radius, and $\lambda$ ($-0.18$ and $-0.23$, respectively). Our results show that modified gravity alone cannot compensate for unrealistic dense-matter physics, highlighting the necessity of realistic EOSs and joint multimessenger constraints, and establish conservative $f(R,T)$ gravity as a viable strong-field extension of General Relativity.