A conservative energy-momentum tensor in the $f(R,T)$ gravity and its implications for the phenomenology of neutron stars

TL;DR

This paper develops a conservative $f(R,T)$ gravity framework to analyze neutron star structure via the TOV equation, revealing a strong link between gravity modifications and star matter properties.

Contribution

It derives a specific form of $h(T)$ ensuring energy-momentum conservation in $f(R,T)$ gravity and applies it to neutron star models with various equations of state.

Findings

Derived a form of $h(T)$ for conserved $f(R,T)$ gravity.

Solved the TOV equation for different equations of state.

Analyzed neutron star properties within this modified gravity framework.

Abstract

The solutions for the Tolmann-Oppenheimer-Volkoff (TOV) equation bring valuable informations about the macroscopical features of compact astrophysical objects as neutron stars. They are sensitive to both the equation of state considered for nuclear matter and the background gravitational theory. In this work we construct the TOV equation for a conservative version of the $f(R,T)$ gravity. While the non-vanishing of the covariant derivative of the $f(R,T)$ energy-momentum tensor yields, in a cosmological perspective, the prediction of creation of matter throughout the universe evolution as shown by T. Harko, in the analysis of the hydrostatic equilibrium of compact astrophysical objects, this property still lacks a convincing physical explanation. The imposition of $\nabla^{\mu}T_{\mu\nu}=0$ demands a particular form for the function $h(T)$ in $f(R,T)=R+h(T)$, which is here derived. Therefore, the choice of a specific equation of state for the star matter demands a unique form of $h(T)$, manifesting a strong connection between conserved $f(R,T)$ gravity and the star matter constitution. We construct and solve the TOV equation for the general equation of state for $p=k\rho^{\Gamma}$, with $k$ being the EoS parameter, $\rho$ {\it the energy density} and $\Gamma$ is the adiabatic index. We also derive the macroscopical properties of neutron stars ($\Gamma=5/3$) within this approach.