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

TL;DR

This paper reformulates $f(R,T)$ gravity to be EoS-independent, deriving new stellar structure equations and comparing neutron star predictions with astrophysical data.

Contribution

It introduces a conservative $f(R,T)$ gravity formulation using an effective energy-momentum tensor, ensuring universality and consistency in neutron star modeling.

Findings

Neutron star mass-radius relations consistent with observations.

Tidal deformability predictions align with GW170817 data.

The reformulation avoids EoS-dependent gravity sector issues.

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.