Physical properties and maximum allowable mass-radius relation of complexity-free compact stellar objects within modified $f(R,T)$ gravity formalism

This paper focuses on investigating the physical properties and predicted radii of compact stars generated by Tolman--IV complexity-free model within the background of modified gravity theory, especially $f(\mathcal{R},T)$-gravity theory, under complexity formalism for a spherically symmetric spacetime proposed by L. Herrera [Phys Rev D 97: 044010, 2018]. By solving the resulting set of differential equations, the explicit forms of the energy-momentum (EM) tensor components, including the density, radial pressure and tangential pressure, are obtained. The influence of the parameter $\chi$ on various physical properties of the star has been thoroughly investigated. The model undergoes a series of rigorous tests to determine its physical relevance. The findings indicate that the model exhibits regularity, stability and features a surface with vanishing pressure. The boundary of this surface is determined by carefully selecting the parameter space. The complexity method employed in $f(\mathcal{R},T)$ gravity offers an interesting approach for developing astrophysical models that are consistent with observable events as demonstrated by recent experiments. In this regard, we present a study that uses observational data from the GW190814 event, detected by the LIGO and Virgo observatories, to investigate the validity of the Tolman-IV model in $f(R, T)$ gravity. The analysis includes comparing the model's predictions with the observed characteristics of the compact object involved in the merger. In addition, data from two-millisecond pulsars, PSR J1614-2230 and PSR J0952-0607, are incorporated to further constrain theoretical theories. However, we present a diagram illustrating the relationship between the total mass and radius of the compact object candidates for different values of a parameter $\chi$.