Neutron stars in a conservative $f(R,T)$ gravity

Abstract

We investigate a conservative formulation of $f(R,T)$ gravity motivated by a key limitation of several existing approaches: the gravitational function is often reconstructed from a chosen equation of state, making the gravity sector EoS-dependent and compromising universality. To avoid this problem, we reformulate the theory in terms of an effective energy-momentum tensor, so that the conservation law follows from the field equations and Bianchi identities while the gravitational action remains independent of the microphysical EoS. We derive the modified stellar structure equations, establish theoretical consistency conditions including coupling bounds and crust-singularity avoidance, and present the tidal perturbation sector in terms of effective thermodynamic variables and an effective sound speed. We then compute neutron star observables using realistic tabulated EoSs, including mass-radius relations and tidal deformabilities, and compare the model with current astrophysical constraints from massive pulsars, NICER radius measurements, and GW170817.