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

. The solutions for the Tolmann-Oppenheimer-Volkoff (TOV) equation bring valuable information 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, in the analysis of the hydrostatic equilibrium of compact astrophysical objects, this property still lacks a convincing physical explanation. The imposition of ∇ μ T μ ν = 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 stellar matter demands a unique form of h ( T ), manifesting a strong connection between conserved f ( R , T ) gravity and the stellar matter constitution. We construct and solve the TOV equation for the general equation of state p = k ρ Γ , with p being the stellar pressure, k the EoS parameter, ρ the energy density and Γ the adiabatic index. We derive the macroscopical properties of neutron stars ( Γ = 5 / 3 ) within this approach and show that their masses are very sensitive to the parameter α that enters in the h ( T ) function, while their radii are not. These conclusions are in contrast with previous works of compact stars in the non-conservative version of the theory, where the stellar masses do not change considerably but the stellar radii exhibit a large increase, not very consistent with the neutron star phenomenology.