Tolman VII (TVII) Solution with Theory of Energy-Momentum Squared Gravity (EMSG) in Neutron Stars

We study the Tolman VII (TVII) solution for the Energy-Momentum Squared Gravity (EMSG) as well as the solution's compatibility with stars properties. We perform a systematic analysis of the suitability of the equation of state (EoS) for energy density and pressure profiles. In calculations, for convenience, all physical quantities are expressed in the form of dimensionless quantities by introducing the quantity ζ = r/R. This dimensionless quantity will be used to determine the ratio between a star's mass and its radius. The TVII solution provides limits on compactness C [0.01, 0.27] and neutron star's mass 2.60M⊙. Having α as a free parameter of the EMSG model gives the new range compactness C [0.01, 0.386] for ζ[0, 1] with α [0.01, ∞] and shows a star mass of 2.97M⊙. The metric eλ effective and the metric eν effective produce the range of α [0.1, 0.6], which represents both metric to be physical.